{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261102-r04-topological-boundary-0001","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 2], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024001,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0002","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 2], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024002,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0003","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024003,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0004","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024004,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0005","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024005,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0006","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024006,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0007","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 2], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024007,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0008","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 2], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024008,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0009","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([2, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024009,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0010","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([2, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024010,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0011","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([2, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024011,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0012","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([2, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024012,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0013","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024013,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0014","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024014,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0015","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([2, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024015,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0016","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([2, 3], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024016,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0017","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([3, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024017,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0018","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([3, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024018,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0019","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024019,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0020","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([1, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024020,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0021","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([2, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024021,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0022","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([2, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024022,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0023","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([3, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024023,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0024","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([3, 4], [1, 2, 3, 4], [], [1, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024024,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0025","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-exact；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,closure,interior,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [0, 2, 3, 4], [], [0, 2, 3, 4])","explanation_zh":"Wave5第二層核對=([0, 2], [0, 2, 3, 4], [], [0, 2, 3, 4])；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-exact","seed":202611024025,"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_topological_boundary","operation":"boundary-exact","semantic_template":"qf-mod33-boundary-exact/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0026","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(0, [1, 2, 3, 4], 否, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024026,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0027","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(1, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024027,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0028","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(3, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(3, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024028,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0029","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(4, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024029,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0030","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(3, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(3, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024030,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0031","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(0, [1, 2, 3, 4], 否, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024031,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0032","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(2, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024032,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0033","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(1, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024033,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0034","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(1, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024034,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0035","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(1, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024035,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0036","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(0, [1, 2, 3, 4], 否, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024036,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0037","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(2, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024037,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0038","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(1, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(1, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024038,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0039","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(4, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024039,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0040","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(4, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024040,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0041","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(0, [1, 2, 3, 4], 否, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024041,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0042","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(3, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(3, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024042,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0043","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(4, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024043,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0044","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(2, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024044,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0045","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(2, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024045,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0046","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(0, [1, 2, 3, 4], 否, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(0, [1, 2, 3, 4], 否, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024046,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0047","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(4, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(4, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024047,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0048","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(3, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(3, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024048,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0049","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(2, [1, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024049,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0050","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-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,boundary,in_boundary,scope] 欄序回答。","answer":{"kind":"expression","value":"(4, [0, 2, 3, 4], 是, topology_relative_boundary)","explanation_zh":"Wave5第二層核對=(4, [0, 2, 3, 4], 是, topology_relative_boundary)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-membership","seed":202611024050,"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_topological_boundary","operation":"boundary-membership","semantic_template":"qf-mod33-boundary-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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0051","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [0, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 2], [0, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024051,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0052","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [0, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 2], [0, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024052,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0053","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [0, 2, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 3], [0, 2, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024053,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0054","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [0, 2, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 3], [0, 2, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024054,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0055","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [0, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 4], [0, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024055,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0056","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [0, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 4], [0, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024056,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0057","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [0, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 2], [0, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024057,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0058","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [0, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 2], [0, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024058,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0059","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 1, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([2, 3], [0, 1, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024059,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0060","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 1, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([2, 3], [0, 1, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024060,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0061","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [0, 1, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([2, 4], [0, 1, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024061,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0062","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [0, 1, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([2, 4], [0, 1, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024062,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0063","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [0, 2, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 3], [0, 2, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024063,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0064","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [0, 2, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 3], [0, 2, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024064,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0065","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 1, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([2, 3], [0, 1, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024065,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0066","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 1, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([2, 3], [0, 1, 4], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024066,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0067","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [0, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([3, 4], [0, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024067,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0068","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [0, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([3, 4], [0, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024068,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0069","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [0, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 4], [0, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024069,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0070","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [0, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([1, 4], [0, 2, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024070,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0071","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [0, 1, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([2, 4], [0, 1, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024071,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0072","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [0, 1, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([2, 4], [0, 1, 3], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024072,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0073","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [0, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([3, 4], [0, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024073,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0074","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [0, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([3, 4], [0, 1, 2], [1, 2, 3, 4], [1, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024074,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0075","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-complement-invariance；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,complement,boundary_a,boundary_complement,equal] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [1, 3, 4], [0, 2, 3, 4], [0, 2, 3, 4], 是)","explanation_zh":"Wave5第二層核對=([0, 2], [1, 3, 4], [0, 2, 3, 4], [0, 2, 3, 4], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-complement-invariance","seed":202611024075,"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_topological_boundary","operation":"boundary-complement-invariance","semantic_template":"qf-mod33-boundary-complement-invariance/{\"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0076","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024076,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0077","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024077,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0078","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024078,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0079","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024079,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,3],[0,1,3,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0080","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024080,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0081","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024081,"parameters":{"n":5,"topology":[[],[0],[0,1],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0082","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024082,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0083","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024083,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,1,2],[0,1,2,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0084","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024084,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,2],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0085","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024085,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,2],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0086","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024086,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0087","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024087,"parameters":{"n":5,"topology":[[],[0],[0,2],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,2],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0088","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024088,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,1,3],[0,1,2,3],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,3],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0090","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024090,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,1,2,3],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,3],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0091","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024091,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,2,3],[0,2,3,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,3],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0092","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024092,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,3],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0093","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024093,"parameters":{"n":5,"topology":[[],[0],[0,3],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0094","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024094,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,2,4],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0095","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024095,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,1,4],[0,1,3,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0096","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024096,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,1,2,4],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0097","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024097,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,2,4],[0,2,3,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0098","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024098,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0099","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],\"which\":\"whole\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(whole, [0, 1, 2, 3, 4], [], 是)","explanation_zh":"Wave5第二層核對=(whole, [0, 1, 2, 3, 4], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024099,"parameters":{"n":5,"topology":[[],[0],[0,4],[0,3,4],[0,2,3,4],[0,1,2,3,4]],"which":"whole","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]],\"which\":\"whole\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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-20261102-r04-topological-boundary-0100","batch_id":"batch-20261014-advance-20261102-r04-topological-boundary-foundations","language":"zh-Hant","source_mko_ids":["mko-topological-boundary"],"title_zh":"拓撲邊界","stem_zh":"完整有限拓撲與同一載體子集。操作=boundary-empty-whole；資料={\"n\":5,\"topology\":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"which\":\"empty\"}。請依 [which,subset,boundary,empty] 欄序回答。","answer":{"kind":"expression","value":"(empty, [], [], 是)","explanation_zh":"Wave5第二層核對=(empty, [], [], 是)；依完整明示資料重算；boundary等於closure扣除interior且與補集boundary相同；空集與全空間boundary為空；結果相對拓撲而非圖形外觀。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["拓撲邊界"]},"variant":{"family_id":"qf-mod33-boundary-empty-whole","seed":202611024100,"parameters":{"n":5,"topology":[[],[1],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"which":"empty","domain":"Complete_finite_topological_boundary","operation":"boundary-empty-whole","semantic_template":"qf-mod33-boundary-empty-whole/{\"n\":5,\"topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]],\"which\":\"empty\"}"}},"verification":{"status":"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、任意維basis theorem、bounded-to-global kernel/image、一般compactness、因果推論、language equivalence、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"}}