{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r03-topological-basis-0001","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[1],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073001,"parameters":{"n":5,"basis":[[0],[1],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0002","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073002,"parameters":{"n":5,"basis":[[0],[0,1],[1],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0003","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073003,"parameters":{"n":5,"basis":[[0],[0,2],[1],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,2],[0],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0004","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073004,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0,2],[0],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0005","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[1],[1,2],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073005,"parameters":{"n":5,"basis":[[0],[1],[1,2],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0],[1,2],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0006","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[1,2],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073006,"parameters":{"n":5,"basis":[[0],[0,1],[1],[1,2],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0],[1,2],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0007","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[1,2],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073007,"parameters":{"n":5,"basis":[[0],[0,2],[1],[1,2],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,2],[0],[1,2],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0008","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073008,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0,2],[0],[1,2],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0009","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[1],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073009,"parameters":{"n":5,"basis":[[0],[1],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0010","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073010,"parameters":{"n":5,"basis":[[0],[0,1],[1],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0011","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073011,"parameters":{"n":5,"basis":[[0],[0,2],[1],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,2],[0],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0012","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073012,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0,2],[0],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0013","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[1],[1,2],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073013,"parameters":{"n":5,"basis":[[0],[1],[1,2],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0014","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[1,2],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073014,"parameters":{"n":5,"basis":[[0],[0,1],[1],[1,2],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0015","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[1,2],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073015,"parameters":{"n":5,"basis":[[0],[0,2],[1],[1,2],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,2],[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0016","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[1,2],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073016,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[1,2],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0,2],[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0017","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[1],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073017,"parameters":{"n":5,"basis":[[0],[1],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0018","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073018,"parameters":{"n":5,"basis":[[0],[0,1],[1],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0019","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073019,"parameters":{"n":5,"basis":[[0],[0,2],[1],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,2],[0],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0020","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073020,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0,2],[0],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0021","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[1],[1,2],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073021,"parameters":{"n":5,"basis":[[0],[1],[1,2],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0022","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[1,2],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073022,"parameters":{"n":5,"basis":[[0],[0,1],[1],[1,2],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0023","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[1,2],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073023,"parameters":{"n":5,"basis":[[0],[0,2],[1],[1,2],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,2],[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0024","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073024,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0,1],[0,2],[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0025","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-basis-qualification；資料={\"n\":5,\"basis\":[[0],[1],[2],[2,3],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, null, 是)","explanation_zh":"Wave6根層核對=(是, 是, null, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-basis-qualification","seed":202611073025,"parameters":{"n":5,"basis":[[0],[1],[2],[2,3],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-basis-qualification","semantic_template":"qf-mod38-topbasis-basis-qualification/{\"basis\":[[0],[1],[2,3],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0026","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[1],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073026,"parameters":{"n":5,"basis":[[0],[1],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0027","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073027,"parameters":{"n":5,"basis":[[0],[0,1],[1],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0028","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073028,"parameters":{"n":5,"basis":[[0],[0,2],[1],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,2],[0],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0029","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073029,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0,2],[0],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0030","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[1],[1,2],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073030,"parameters":{"n":5,"basis":[[0],[1],[1,2],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0],[1,2],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0031","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[1,2],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073031,"parameters":{"n":5,"basis":[[0],[0,1],[1],[1,2],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0],[1,2],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0032","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[1,2],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073032,"parameters":{"n":5,"basis":[[0],[0,2],[1],[1,2],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,2],[0],[1,2],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0033","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073033,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0,2],[0],[1,2],[1],[2],[3],[4]],\"n\":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-r03-topological-basis-0034","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[1],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073034,"parameters":{"n":5,"basis":[[0],[1],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0035","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073035,"parameters":{"n":5,"basis":[[0],[0,1],[1],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0036","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073036,"parameters":{"n":5,"basis":[[0],[0,2],[1],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,2],[0],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0037","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073037,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0,2],[0],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0038","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[1],[1,2],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073038,"parameters":{"n":5,"basis":[[0],[1],[1,2],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0039","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[1,2],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073039,"parameters":{"n":5,"basis":[[0],[0,1],[1],[1,2],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0040","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[1,2],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073040,"parameters":{"n":5,"basis":[[0],[0,2],[1],[1,2],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,2],[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0041","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[1,2],[2],[2,3],[3],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073041,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[1,2],[2],[2,3],[3],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0,2],[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":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-r03-topological-basis-0042","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[1],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073042,"parameters":{"n":5,"basis":[[0],[1],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0043","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073043,"parameters":{"n":5,"basis":[[0],[0,1],[1],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0044","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073044,"parameters":{"n":5,"basis":[[0],[0,2],[1],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,2],[0],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0045","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073045,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0,2],[0],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0046","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[1],[1,2],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073046,"parameters":{"n":5,"basis":[[0],[1],[1,2],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0047","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[1,2],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073047,"parameters":{"n":5,"basis":[[0],[0,1],[1],[1,2],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0048","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[1,2],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073048,"parameters":{"n":5,"basis":[[0],[0,2],[1],[1,2],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,2],[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0049","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073049,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0,1],[0,2],[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0050","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-generated-topology；資料={\"n\":5,\"basis\":[[0],[1],[2],[2,3],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)","explanation_zh":"Wave6根層核對=([[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3], [0, 1, 2, 3, 4], [0, 1, 2, 4], [0, 1, 3], [0, 1, 3, 4], [0, 1, 4], [0, 2], [0, 2, 3], [0, 2, 3, 4], [0, 2, 4], [0, 3], [0, 3, 4], [0, 4], [1], [1, 2], [1, 2, 3], [1, 2, 3, 4], [1, 2, 4], [1, 3], [1, 3, 4], [1, 4], [2], [2, 3], [2, 3, 4], [2, 4], [3], [3, 4], [4]], 32, 是, all_unions_of_basis_elements)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-generated-topology","seed":202611073050,"parameters":{"n":5,"basis":[[0],[1],[2],[2,3],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-generated-topology","semantic_template":"qf-mod38-topbasis-generated-topology/{\"basis\":[[0],[1],[2,3],[2],[3,4],[3],[4]],\"n\":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-r03-topological-basis-0051","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[1],[2],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073051,"parameters":{"n":5,"basis":[[0],[1],[2],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0],[1],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0052","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[2],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073052,"parameters":{"n":5,"basis":[[0],[0,1],[1],[2],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0],[1],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0053","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[2],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073053,"parameters":{"n":5,"basis":[[0],[0,2],[1],[2],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,2],[0],[1],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0054","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[2],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073054,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[2],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0,2],[0],[1],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0055","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[1],[1,2],[2],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073055,"parameters":{"n":5,"basis":[[0],[1],[1,2],[2],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0],[1,2],[1],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0056","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[1,2],[2],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073056,"parameters":{"n":5,"basis":[[0],[0,1],[1],[1,2],[2],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0],[1,2],[1],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0057","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[1,2],[2],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073057,"parameters":{"n":5,"basis":[[0],[0,2],[1],[1,2],[2],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,2],[0],[1,2],[1],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0058","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073058,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0,2],[0],[1,2],[1],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0059","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[1],[2],[2,3],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073059,"parameters":{"n":5,"basis":[[0],[1],[2],[2,3],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0],[1],[2,3],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0060","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[2],[2,3],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073060,"parameters":{"n":5,"basis":[[0],[0,1],[1],[2],[2,3],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0],[1],[2,3],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0061","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[2],[2,3],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073061,"parameters":{"n":5,"basis":[[0],[0,2],[1],[2],[2,3],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,2],[0],[1],[2,3],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0062","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[2],[2,3],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073062,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[2],[2,3],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0,2],[0],[1],[2,3],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0063","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[1],[1,2],[2],[2,3],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073063,"parameters":{"n":5,"basis":[[0],[1],[1,2],[2],[2,3],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0064","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[1,2],[2],[2,3],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073064,"parameters":{"n":5,"basis":[[0],[0,1],[1],[1,2],[2],[2,3],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0065","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[1,2],[2],[2,3],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073065,"parameters":{"n":5,"basis":[[0],[0,2],[1],[1,2],[2],[2,3],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,2],[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0066","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[1,2],[2],[2,3],[3],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073066,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[1,2],[2],[2,3],[3],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0,2],[0],[1,2],[1],[2,3],[2],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0067","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[1],[2],[3],[3,4],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073067,"parameters":{"n":5,"basis":[[0],[1],[2],[3],[3,4],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0],[1],[2],[3,4],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0068","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[2],[3],[3,4],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073068,"parameters":{"n":5,"basis":[[0],[0,1],[1],[2],[3],[3,4],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0],[1],[2],[3,4],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0069","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[2],[3],[3,4],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073069,"parameters":{"n":5,"basis":[[0],[0,2],[1],[2],[3],[3,4],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,2],[0],[1],[2],[3,4],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0070","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[2],[3],[3,4],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073070,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[2],[3],[3,4],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0,2],[0],[1],[2],[3,4],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0071","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[1],[1,2],[2],[3],[3,4],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073071,"parameters":{"n":5,"basis":[[0],[1],[1,2],[2],[3],[3,4],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0072","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[1],[1,2],[2],[3],[3,4],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073072,"parameters":{"n":5,"basis":[[0],[0,1],[1],[1,2],[2],[3],[3,4],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0073","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,2],[1],[1,2],[2],[3],[3,4],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073073,"parameters":{"n":5,"basis":[[0],[0,2],[1],[1,2],[2],[3],[3,4],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,2],[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0074","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[3,4],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073074,"parameters":{"n":5,"basis":[[0],[0,1],[0,2],[1],[1,2],[2],[3],[3,4],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0,1],[0,2],[0],[1,2],[1],[2],[3,4],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0075","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-existing-topology-audit；資料={\"n\":5,\"basis\":[[0],[1],[2],[2,3],[3],[3,4],[4]],\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 是, 是, 是, 是)","explanation_zh":"Wave6根層核對=(是, 是, 是, 是, 是)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-existing-topology-audit","seed":202611073075,"parameters":{"n":5,"basis":[[0],[1],[2],[2,3],[3],[3,4],[4]],"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,1,2,4],[0,1,3],[0,1,3,4],[0,1,4],[0,2],[0,2,3],[0,2,3,4],[0,2,4],[0,3],[0,3,4],[0,4],[1],[1,2],[1,2,3],[1,2,3,4],[1,2,4],[1,3],[1,3,4],[1,4],[2],[2,3],[2,3,4],[2,4],[3],[3,4],[4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-existing-topology-audit","semantic_template":"qf-mod38-topbasis-existing-topology-audit/{\"basis\":[[0],[1],[2,3],[2],[3,4],[3],[4]],\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2,4],[0,1,2],[0,1,3,4],[0,1,3],[0,1,4],[0,1],[0,2,3,4],[0,2,3],[0,2,4],[0,2],[0,3,4],[0,3],[0,4],[0],[1,2,3,4],[1,2,3],[1,2,4],[1,2],[1,3,4],[1,3],[1,4],[1],[2,3,4],[2,3],[2,4],[2],[3,4],[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-r03-topological-basis-0076","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[1,2],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073076,"parameters":{"n":5,"basis":[[0,1],[1,2],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[1,2],[2,3],[3,4]],\"n\":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-r03-topological-basis-0077","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[1,2],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073077,"parameters":{"n":5,"basis":[[0,1],[0,2],[1,2],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[1,2],[2,3],[3,4]],\"n\":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-r03-topological-basis-0078","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[1,2],[1,3],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073078,"parameters":{"n":5,"basis":[[0,1],[1,2],[1,3],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[1,2],[1,3],[2,3],[3,4]],\"n\":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-r03-topological-basis-0079","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073079,"parameters":{"n":5,"basis":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[1,2],[1,3],[2,3],[3,4]],\"n\":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-r03-topological-basis-0080","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[1,2],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073080,"parameters":{"n":5,"basis":[[0,1],[1,2],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[1,2],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0081","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073081,"parameters":{"n":5,"basis":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[1,2],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0082","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073082,"parameters":{"n":5,"basis":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0083","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073083,"parameters":{"n":5,"basis":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0084","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,3],[1,2],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073084,"parameters":{"n":5,"basis":[[0,1],[0,3],[1,2],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,3],[1,2],[2,3],[3,4]],\"n\":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-r03-topological-basis-0085","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073085,"parameters":{"n":5,"basis":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[0,3],[1,2],[2,3],[3,4]],\"n\":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-r03-topological-basis-0086","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073086,"parameters":{"n":5,"basis":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":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-r03-topological-basis-0087","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073087,"parameters":{"n":5,"basis":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[3,4]],\"n\":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-r03-topological-basis-0088","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073088,"parameters":{"n":5,"basis":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0089","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073089,"parameters":{"n":5,"basis":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[0,3],[1,2],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0090","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073090,"parameters":{"n":5,"basis":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0091","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073091,"parameters":{"n":5,"basis":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0092","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[1,2],[1,4],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073092,"parameters":{"n":5,"basis":[[0,1],[1,2],[1,4],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[1,2],[1,4],[2,3],[3,4]],\"n\":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-r03-topological-basis-0093","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073093,"parameters":{"n":5,"basis":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[1,2],[1,4],[2,3],[3,4]],\"n\":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-r03-topological-basis-0094","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073094,"parameters":{"n":5,"basis":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":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-r03-topological-basis-0095","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073095,"parameters":{"n":5,"basis":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[3,4]],\"n\":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-r03-topological-basis-0096","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073096,"parameters":{"n":5,"basis":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[1,2],[1,4],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0097","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[1,2],[1,4],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073097,"parameters":{"n":5,"basis":[[0,1],[0,2],[1,2],[1,4],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[1,2],[1,4],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0098","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073098,"parameters":{"n":5,"basis":[[0,1],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0099","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073099,"parameters":{"n":5,"basis":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,2],[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]],\"n\":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-r03-topological-basis-0100","batch_id":"batch-20261014-advance-20261107-r03-topological-basis-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-basis"],"title_zh":"拓撲基底","stem_zh":"完整有限carrier與完整basis candidate。操作=topbasis-subbasis-boundary；資料={\"n\":5,\"basis\":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)","explanation_zh":"Wave6根層核對=(是, 否, 否, 否, cover_without_local_intersection_refinement_is_not_a_basis_and_may_only_be_a_subbasis)；依完整明示資料獨立重算；basis須覆蓋X並逐點滿足局部交細化；basis elements皆為X子集；相對既有拓撲還須basis elements開且每個開集為basis聯集；basis不可混同subbasis。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲基底"]},"variant":{"family_id":"qf-mod38-topbasis-subbasis-boundary","seed":202611073100,"parameters":{"n":5,"basis":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],"domain":"Complete_finite_topological_basis","operation":"topbasis-subbasis-boundary","semantic_template":"qf-mod38-topbasis-subbasis-boundary/{\"basis\":[[0,1],[0,3],[1,2],[1,4],[2,3],[3,4]],\"n\":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"}}