{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0001","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,2]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 2], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012001,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,2],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0002","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,2]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 2], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012002,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[1,2],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0003","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012003,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0004","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,3]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012004,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"subset":[1,3],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0005","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012005,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[1,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0006","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012006,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[1,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0007","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,2]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 2], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012007,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,2],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0008","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,2]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 2], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012008,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[1,2],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0009","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[2,3]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([2, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012009,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"subset":[2,3],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0010","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,3]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([2, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012010,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"subset":[2,3],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0011","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[2,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([2, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012011,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[2,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0012","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([2, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012012,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"subset":[2,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0013","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012013,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0014","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,3]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012014,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"subset":[1,3],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0015","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[2,3]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([2, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012015,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"subset":[2,3],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0016","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,3]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([2, 3], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012016,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"subset":[2,3],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0017","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[3,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([3, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012017,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"subset":[3,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0018","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[3,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([3, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012018,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[3,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0019","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012019,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[1,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0020","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([1, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012020,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[1,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0021","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[2,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([2, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012021,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[2,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0022","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([2, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012022,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"subset":[2,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0023","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[3,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([3, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012023,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"subset":[3,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0024","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[3,4]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([3, 4], [[0, 1, 2, 3, 4], [1, 2, 3, 4]], [1, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012024,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[3,4],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0025","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure；資料={\"n\":5,\"topology\":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[0,2]}。請依 [subset,closed_supersets,closure] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 1, 2, 3, 4], [0, 2, 3, 4]], [0, 2, 3, 4])","explanation_zh":"Wave5根節點核對=([0, 2], [[0, 1, 2, 3, 4], [0, 2, 3, 4]], [0, 2, 3, 4])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure","seed":202611012025,"parameters":{"n":5,"topology":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[0,2],"domain":"Complete_finite_topology_subset","operation":"topology-closure","semantic_template":"qf-mod32-topology-closure/{\"n\":5,\"subset\":[0,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0026","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,2]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 2], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012026,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,2],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0027","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,2]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 2], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012027,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[1,2],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0028","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 3], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012028,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0029","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,3]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 3], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012029,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"subset":[1,3],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0030","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012030,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[1,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0031","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012031,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[1,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0032","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,2]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 2], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012032,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,2],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0033","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,2]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 2], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012033,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[1,2],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0036","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[2,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([2, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012036,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[2,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0043","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[3,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([3, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012043,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[3,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0044","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012044,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[1,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0045","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([1, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012045,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[1,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0046","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[2,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([2, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012046,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[2,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0047","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([2, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012047,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"subset":[2,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0048","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[3,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([3, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012048,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"subset":[3,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0049","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[3,4]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [[]], [])","explanation_zh":"Wave5根節點核對=([3, 4], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012049,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[3,4],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0050","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior；資料={\"n\":5,\"topology\":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[0,2]}。請依 [subset,open_subsets,interior] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[]], [])","explanation_zh":"Wave5根節點核對=([0, 2], [[]], [])；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior","seed":202611012050,"parameters":{"n":5,"topology":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[0,2],"domain":"Complete_finite_topology_subset","operation":"topology-interior","semantic_template":"qf-mod32-topology-interior/{\"n\":5,\"subset\":[0,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0051","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,2],\"point\":0}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(0, [1, 2, 3, 4], 否, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012051,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,2],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":0,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0052","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,2],\"point\":1}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(1, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012052,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[1,2],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":1,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0053","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3],\"point\":3}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(3, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012053,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3],"point":3,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":3,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0054","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,3],\"point\":4}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(4, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012054,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"subset":[1,3],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":4,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0055","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,4],\"point\":3}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(3, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012055,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[1,4],"point":3,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":3,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0056","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,4],\"point\":0}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(0, [1, 2, 3, 4], 否, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012056,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[1,4],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":0,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0057","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,2],\"point\":2}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(2, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012057,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,2],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":2,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0058","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,2],\"point\":1}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(1, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012058,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[1,2],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":1,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0059","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[2,3],\"point\":1}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(1, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012059,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"subset":[2,3],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":1,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0060","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,3],\"point\":1}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(1, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012060,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"subset":[2,3],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":1,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0061","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[2,4],\"point\":0}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(0, [1, 2, 3, 4], 否, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012061,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[2,4],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":0,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0062","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,4],\"point\":2}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(2, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012062,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"subset":[2,4],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":2,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0063","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3],\"point\":1}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(1, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012063,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":1,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0064","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,3],\"point\":4}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(4, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012064,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"subset":[1,3],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":4,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0065","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[2,3],\"point\":4}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(4, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012065,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"subset":[2,3],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":4,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0066","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,3],\"point\":0}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(0, [1, 2, 3, 4], 否, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012066,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"subset":[2,3],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":0,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0067","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[3,4],\"point\":3}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(3, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012067,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"subset":[3,4],"point":3,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":3,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0068","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[3,4],\"point\":4}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(4, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012068,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[3,4],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":4,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0069","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,4],\"point\":2}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(2, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012069,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[1,4],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":2,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0070","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,4],\"point\":2}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(2, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012070,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[1,4],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":2,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0071","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[2,4],\"point\":0}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(0, [1, 2, 3, 4], 否, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012071,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[2,4],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":0,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0072","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,4],\"point\":4}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(4, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012072,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"subset":[2,4],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":4,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0073","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[3,4],\"point\":3}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(3, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012073,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"subset":[3,4],"point":3,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":3,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0074","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[3,4],\"point\":2}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(2, [1, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012074,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[3,4],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":2,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0075","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-closure-membership；資料={\"n\":5,\"topology\":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[0,2],\"point\":4}。請依 [point,closure,in_closure,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [0, 2, 3, 4], 是, topology_relative_closure)","explanation_zh":"Wave5根節點核對=(4, [0, 2, 3, 4], 是, topology_relative_closure)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-closure-membership","seed":202611012075,"parameters":{"n":5,"topology":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[0,2],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-closure-membership","semantic_template":"qf-mod32-topology-closure-membership/{\"n\":5,\"point\":4,\"subset\":[0,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0076","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,2],\"point\":0}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(0, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012076,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,2],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":0,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0077","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,2],\"point\":1}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(1, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012077,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[1,2],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":1,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0078","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3],\"point\":3}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(3, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012078,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3],"point":3,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":3,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0079","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,3],\"point\":4}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(4, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012079,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"subset":[1,3],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":4,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0080","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,4],\"point\":3}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(3, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012080,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[1,4],"point":3,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":3,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0081","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,4],\"point\":0}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(0, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012081,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[1,4],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":0,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0082","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,2],\"point\":2}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(2, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012082,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,2],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":2,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0083","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,2],\"point\":1}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(1, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012083,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"subset":[1,2],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":1,\"subset\":[1,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0084","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[2,3],\"point\":1}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(1, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012084,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"subset":[2,3],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":1,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0085","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,3],\"point\":1}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(1, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012085,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"subset":[2,3],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":1,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0086","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[2,4],\"point\":0}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(0, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012086,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[2,4],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":0,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0087","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,4],\"point\":2}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(2, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012087,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"subset":[2,4],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":2,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,2],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0088","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3],\"point\":1}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(1, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012088,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3],"point":1,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":1,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0089","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,3],\"point\":4}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(4, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012089,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"subset":[1,3],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":4,\"subset\":[1,3],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0090","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],\"subset\":[2,3],\"point\":4}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(4, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012090,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"subset":[2,3],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":4,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0091","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,3],\"point\":0}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(0, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012091,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"subset":[2,3],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":0,\"subset\":[2,3],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0092","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[3,4],\"point\":3}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(3, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012092,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"subset":[3,4],"point":3,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":3,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0093","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[3,4],\"point\":4}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(4, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012093,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[3,4],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":4,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0094","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[1,4],\"point\":2}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(2, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012094,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"subset":[1,4],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":2,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0095","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[1,4],\"point\":2}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(2, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012095,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"subset":[1,4],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":2,\"subset\":[1,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0096","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"subset\":[2,4],\"point\":0}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(0, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012096,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"subset":[2,4],"point":0,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":0,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0097","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[2,4],\"point\":4}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(4, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012097,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"subset":[2,4],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":4,\"subset\":[2,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0098","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],\"subset\":[3,4],\"point\":3}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(3, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012098,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"subset":[3,4],"point":3,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":3,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0099","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"subset\":[3,4],\"point\":2}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(2, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012099,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"subset":[3,4],"point":2,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":2,\"subset\":[3,4],\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r02-closure-and-interior-0100","batch_id":"batch-20261014-advance-20261101-r02-closure-and-interior-foundations","language":"zh-Hant","source_mko_ids":["mko-closure-and-interior"],"title_zh":"閉包與內部","stem_zh":"完整有限拓撲與同一載體子集。操作=topology-interior-membership；資料={\"n\":5,\"topology\":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[0,2],\"point\":4}。請依 [point,interior,in_interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, [], 否, topology_relative_interior)","explanation_zh":"Wave5根節點核對=(4, [], 否, topology_relative_interior)；依完整明示資料重算；閉包取全部閉超集之交且內部取全部開子集之聯；結果相對指定拓撲；未供度量時不使用度量推論。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["閉包與內部"]},"variant":{"family_id":"qf-mod32-topology-interior-membership","seed":202611012100,"parameters":{"n":5,"topology":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[0,2],"point":4,"domain":"Complete_finite_topology_subset","operation":"topology-interior-membership","semantic_template":"qf-mod32-topology-interior-membership/{\"n\":5,\"point\":4,\"subset\":[0,2],\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般compactness／a.s.定理／maximum matching／語言等價、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}