{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0001","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[0],[0,1],[0,1,2],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181001,"parameters":{"n":4,"opens":[[0],[0,1],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[0],[0,1],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0002","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[1],[0,1],[0,1,2]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [0, 1], [0, 1, 2]], 是, 否, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [1], [0, 1], [0, 1, 2]], 是, 否, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181002,"parameters":{"n":4,"opens":[[],[1],[0,1],[0,1,2]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[1],[0,1],[0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0003","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[2],[0,2],[0,1,2],[3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [0, 2], [0, 1, 2], [3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[2], [3], [2, 3]], 無)","explanation_zh":"擴展基礎核對=(4, [[], [2], [0, 2], [0, 1, 2], [3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[2], [3], [2, 3]], 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181003,"parameters":{"n":4,"opens":[[],[2],[0,2],[0,1,2],[3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[2],[0,2],[0,1,2],[3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0004","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181004,"parameters":{"n":4,"opens":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0005","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[0],[0,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181005,"parameters":{"n":4,"opens":[[0],[0,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[0],[0,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0006","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[1],[1,2],[0,1,2]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 2], [0, 1, 2]], 是, 否, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 2], [0, 1, 2]], 是, 否, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181006,"parameters":{"n":4,"opens":[[],[1],[1,2],[0,1,2]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[1],[1,2],[0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0007","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[2],[1,2],[0,1,2],[3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [1, 2], [0, 1, 2], [3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[2], [3], [2, 3]], 無)","explanation_zh":"擴展基礎核對=(4, [[], [2], [1, 2], [0, 1, 2], [3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[2], [3], [2, 3]], 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181007,"parameters":{"n":4,"opens":[[],[2],[1,2],[0,1,2],[3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[2],[1,2],[0,1,2],[3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0008","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181008,"parameters":{"n":4,"opens":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0009","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[0],[0,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181009,"parameters":{"n":4,"opens":[[0],[0,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[0],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0010","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[1],[1,3],[0,1,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 3], [0, 1, 3]], 是, 否, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 3], [0, 1, 3]], 是, 否, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181010,"parameters":{"n":4,"opens":[[],[1],[1,3],[0,1,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[1],[1,3],[0,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0011","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[1],[2],[2,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[1], [2], [1, 2]], 無)","explanation_zh":"擴展基礎核對=(4, [[], [1], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[1], [2], [1, 2]], 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181011,"parameters":{"n":4,"opens":[[],[1],[2],[2,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[1],[2],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0012","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181012,"parameters":{"n":4,"opens":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0013","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[0],[0,1],[0,1,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181013,"parameters":{"n":4,"opens":[[0],[0,1],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[0],[0,1],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0014","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[1],[0,1],[0,1,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [0, 1], [0, 1, 3]], 是, 否, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [1], [0, 1], [0, 1, 3]], 是, 否, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181014,"parameters":{"n":4,"opens":[[],[1],[0,1],[0,1,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[1],[0,1],[0,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0015","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[1],[2],[0,2],[0,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[1], [2], [1, 2]], 無)","explanation_zh":"擴展基礎核對=(4, [[], [1], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[1], [2], [1, 2]], 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181015,"parameters":{"n":4,"opens":[[],[1],[2],[0,2],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[1],[2],[0,2],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0016","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181016,"parameters":{"n":4,"opens":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0017","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[0],[0,2],[0,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181017,"parameters":{"n":4,"opens":[[0],[0,2],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[0],[0,2],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0018","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[1],[1,2],[1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 2], [1, 2, 3]], 是, 否, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 2], [1, 2, 3]], 是, 否, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181018,"parameters":{"n":4,"opens":[[],[1],[1,2],[1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[1],[1,2],[1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0019","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[0],[2],[1,2],[1,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[0], [2], [0, 2]], 無)","explanation_zh":"擴展基礎核對=(4, [[], [0], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[0], [2], [0, 2]], 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181019,"parameters":{"n":4,"opens":[[],[0],[2],[1,2],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[0],[2],[1,2],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0020","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181020,"parameters":{"n":4,"opens":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0021","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[0],[0,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 否, 是, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181021,"parameters":{"n":4,"opens":[[0],[0,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[0],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0022","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[1],[1,3],[1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 3], [1, 2, 3]], 是, 否, 是, 是, 否, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 3], [1, 2, 3]], 是, 否, 是, 是, 否, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181022,"parameters":{"n":4,"opens":[[],[1],[1,3],[1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[1],[1,3],[1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0023","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[0],[2],[2,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[0], [2], [0, 2]], 無)","explanation_zh":"擴展基礎核對=(4, [[], [0], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 是, 否, 是, 否, [[0], [2], [0, 2]], 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181023,"parameters":{"n":4,"opens":[[],[0],[2],[2,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[0],[2],[2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0024","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":4,\"opens\":[[],[3],[2,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)","explanation_zh":"擴展基礎核對=(4, [[], [3], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 是, 是, 是, 是, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181024,"parameters":{"n":4,"opens":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":4,\"opens\":[[],[3],[2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0025","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-axiom-audit；資料={\"n\":3,\"opens\":[[],[0],[0,1],[0,1,2]]}。請依 [n,opens,empty,full,union_closed,intersection_closed,topology,union_counterexample,intersection_counterexample] 的欄序回答。","answer":{"kind":"expression","value":"(3, [[], [0], [0, 1], [0, 1, 2]], 是, 是, 是, 是, 是, 無, 無)","explanation_zh":"擴展基礎核對=(3, [[], [0], [0, 1], [0, 1, 2]], 是, 是, 是, 是, 是, 無, 無)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-axiom-audit","seed":202610181025,"parameters":{"n":3,"opens":[[],[0],[0,1],[0,1,2]],"domain":"Fin_topology_family","operation":"topology-axiom-audit","semantic_template":"qf-ext18-topology-axiom-audit/{\"n\":3,\"opens\":[[],[0],[0,1],[0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0026","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[0],[0,1],[0,1,2],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181026,"parameters":{"n":4,"opens":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[0],[0,1],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0027","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[1],[0,1],[0,1,2],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [1], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181027,"parameters":{"n":4,"opens":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[1],[0,1],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0028","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[2],[0,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [2], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181028,"parameters":{"n":4,"opens":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[2],[0,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0029","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181029,"parameters":{"n":4,"opens":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0030","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[0],[0,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181030,"parameters":{"n":4,"opens":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[0],[0,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0031","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[1],[1,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181031,"parameters":{"n":4,"opens":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[1],[1,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0032","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[2],[1,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [2], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181032,"parameters":{"n":4,"opens":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[2],[1,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0033","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181033,"parameters":{"n":4,"opens":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0034","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[0],[0,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181034,"parameters":{"n":4,"opens":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[0],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0035","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[1],[1,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181035,"parameters":{"n":4,"opens":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[1],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0036","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[2],[2,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181036,"parameters":{"n":4,"opens":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[2],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0037","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181037,"parameters":{"n":4,"opens":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0038","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[0],[0,1],[0,1,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181038,"parameters":{"n":4,"opens":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[0],[0,1],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0039","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[1],[0,1],[0,1,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [1], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181039,"parameters":{"n":4,"opens":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[1],[0,1],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0040","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[2],[0,2],[0,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [1, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [1, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181040,"parameters":{"n":4,"opens":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[2],[0,2],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0041","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [1, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181041,"parameters":{"n":4,"opens":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0042","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[0],[0,2],[0,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [1, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [1, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181042,"parameters":{"n":4,"opens":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[0],[0,2],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0043","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[1],[1,2],[1,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181043,"parameters":{"n":4,"opens":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[1],[1,2],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0044","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[2],[1,2],[1,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181044,"parameters":{"n":4,"opens":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[2],[1,2],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0045","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181045,"parameters":{"n":4,"opens":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0046","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[0],[0,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], [[], [1], [1, 2], [1, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181046,"parameters":{"n":4,"opens":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[0],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0047","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[1],[1,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181047,"parameters":{"n":4,"opens":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[1],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0048","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[2],[2,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181048,"parameters":{"n":4,"opens":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[2],[2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0049","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":4,\"opens\":[[],[3],[2,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])","explanation_zh":"擴展基礎核對=(4, [[], [3], [2, 3], [1, 2, 3], [0, 1, 2, 3]], [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [0, 1, 2, 3]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181049,"parameters":{"n":4,"opens":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":4,\"opens\":[[],[3],[2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0050","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-open-closed-inventory；資料={\"n\":3,\"opens\":[[],[0],[0,1],[0,1,2]]}。請依 [n,opens,closed,clopen] 的欄序回答。","answer":{"kind":"expression","value":"(3, [[], [0], [0, 1], [0, 1, 2]], [[], [2], [1, 2], [0, 1, 2]], [[], [0, 1, 2]])","explanation_zh":"擴展基礎核對=(3, [[], [0], [0, 1], [0, 1, 2]], [[], [2], [1, 2], [0, 1, 2]], [[], [0, 1, 2]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-open-closed-inventory","seed":202610181050,"parameters":{"n":3,"opens":[[],[0],[0,1],[0,1,2]],"domain":"Fin_topology_family","operation":"topology-open-closed-inventory","semantic_template":"qf-ext18-topology-open-closed-inventory/{\"n\":3,\"opens\":[[],[0],[0,1],[0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0051","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [1], [0, 1], [2], [0, 2], [1, 2], [0, 1, 2], [3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 離散)","explanation_zh":"擴展基礎核對=(4, [[], [0], [1], [0, 1], [2], [0, 2], [1, 2], [0, 1, 2], [3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 離散)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181051,"parameters":{"n":4,"opens":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0052","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], 是, 不可分)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], 是, 不可分)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181052,"parameters":{"n":4,"opens":[[],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0053","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[0],[0,1],[0,1,2],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181053,"parameters":{"n":4,"opens":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[0],[0,1],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0054","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[1],[0,1],[0,1,2],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [1], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181054,"parameters":{"n":4,"opens":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[1],[0,1],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0055","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[2],[0,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [2], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181055,"parameters":{"n":4,"opens":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[2],[0,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0056","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181056,"parameters":{"n":4,"opens":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0057","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[0],[0,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181057,"parameters":{"n":4,"opens":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[0],[0,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0058","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[1],[1,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181058,"parameters":{"n":4,"opens":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[1],[1,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0059","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[2],[1,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [1, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [2], [1, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181059,"parameters":{"n":4,"opens":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[2],[1,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0060","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181060,"parameters":{"n":4,"opens":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0061","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[0],[0,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181061,"parameters":{"n":4,"opens":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[0],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0062","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[1],[1,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181062,"parameters":{"n":4,"opens":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[1],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0063","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[2],[2,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181063,"parameters":{"n":4,"opens":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[2],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0064","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181064,"parameters":{"n":4,"opens":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0065","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[0],[0,1],[0,1,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181065,"parameters":{"n":4,"opens":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[0],[0,1],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0066","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[1],[0,1],[0,1,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [1], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181066,"parameters":{"n":4,"opens":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[1],[0,1],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0067","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[2],[0,2],[0,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181067,"parameters":{"n":4,"opens":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[2],[0,2],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0068","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181068,"parameters":{"n":4,"opens":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0069","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[0],[0,2],[0,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181069,"parameters":{"n":4,"opens":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[0],[0,2],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0070","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[1],[1,2],[1,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181070,"parameters":{"n":4,"opens":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[1],[1,2],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0071","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[2],[1,2],[1,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181071,"parameters":{"n":4,"opens":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[2],[1,2],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0072","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181072,"parameters":{"n":4,"opens":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0073","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[0],[0,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181073,"parameters":{"n":4,"opens":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[0],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0074","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[1],[1,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [1], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [1], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181074,"parameters":{"n":4,"opens":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[1],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0075","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-discrete-indiscrete；資料={\"n\":4,\"opens\":[[],[2],[2,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens,topology,classification] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)","explanation_zh":"擴展基礎核對=(4, [[], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 其他拓撲)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-discrete-indiscrete","seed":202610181075,"parameters":{"n":4,"opens":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-discrete-indiscrete","semantic_template":"qf-ext18-topology-discrete-indiscrete/{\"n\":4,\"opens\":[[],[2],[2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0076","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,1],[0,1,2],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181076,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,1],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0077","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[0,1],[0,1,2],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [1], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [1], [0, 1], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181077,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[1],[0,1],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[0,1],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0078","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[0,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [2], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [2], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181078,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[2],[0,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[0,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0079","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [3], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181079,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[3],[0,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0080","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [0], [0, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181080,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[0],[0,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0081","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[1,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [1], [1, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [1], [1, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181081,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[1],[1,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[1,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0082","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[1,2],[0,1,2],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [2], [1, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [2], [1, 2], [0, 1, 2], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181082,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[2],[1,2],[0,1,2],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[1,2],[0,1,2],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0083","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [3], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181083,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[3],[1,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0084","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [0], [0, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181084,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[0],[0,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0085","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[1,3],[0,1,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [1], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [1], [1, 3], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181085,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[1],[1,3],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[1,3],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0086","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[2,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [2], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181086,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[2],[2,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0087","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [3], [2, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181087,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[3],[2,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[2,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0088","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,1],[0,1,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [0], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181088,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[0],[0,1],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,1],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0089","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[0,1],[0,1,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [1], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [1], [0, 1], [0, 1, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181089,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[1],[0,1],[0,1,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[0,1],[0,1,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0090","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[0,2],[0,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [2], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181090,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[2],[0,2],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[0,2],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0091","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [3], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181091,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[3],[0,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0092","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,2],[0,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [0], [0, 2], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181092,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[0],[0,2],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,2],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0093","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[1,2],[1,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [1], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [1], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181093,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[1],[1,2],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[1,2],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0094","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[1,2],[1,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [2], [1, 2], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181094,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[2],[1,2],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[1,2],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0095","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [3], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181095,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[3],[1,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0096","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,3],[0,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [0], [0, 3], [0, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181096,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[0],[0,3],[0,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[0],[0,3],[0,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0097","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[1,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [1], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [1], [1, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181097,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[1],[1,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[1],[1,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0098","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[2,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [2], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181098,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[2],[2,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[2],[2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0099","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[2,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0, 1, 2, 3]], [[], [3], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0, 1, 2, 3]], [[], [3], [2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181099,"parameters":{"n":4,"opens_a":[[],[0,1,2,3]],"opens_b":[[],[3],[2,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0,1,2,3]],\"opens_b\":[[],[3],[2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r01-topological-space-0100","batch_id":"batch-20261013-advance-20261018-r01-topological-space-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-space"],"title_zh":"有限拓撲完整核對","stem_zh":"有限底集合完整資料。操作=topology-finer-coarser；資料={\"n\":4,\"opens_a\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_b\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}。請依 [n,opens_A,opens_B,A_subset_B,B_subset_A,relation] 的欄序回答。","answer":{"kind":"expression","value":"(4, [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [0], [1], [0, 1], [2], [0, 2], [1, 2], [0, 1, 2], [3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)","explanation_zh":"擴展基礎核對=(4, [[], [0], [0, 1], [0, 1, 2], [0, 1, 2, 3]], [[], [0], [1], [0, 1], [2], [0, 2], [1, 2], [0, 1, 2], [3], [0, 3], [1, 3], [0, 1, 3], [2, 3], [0, 2, 3], [1, 2, 3], [0, 1, 2, 3]], 是, 否, A較粗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；抽查不構成拓撲公理；開集族與底集合分離。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限拓撲完整核對"]},"variant":{"family_id":"qf-ext18-topology-finer-coarser","seed":202610181100,"parameters":{"n":4,"opens_a":[[],[0],[0,1],[0,1,2],[0,1,2,3]],"opens_b":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"domain":"Fin_topology_family","operation":"topology-finer-coarser","semantic_template":"qf-ext18-topology-finer-coarser/{\"n\":4,\"opens_a\":[[],[0],[0,1],[0,1,2],[0,1,2,3]],\"opens_b\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}