{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0001","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], [[], [1], [1, 3], [1, 3, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 3, 4], [[], [1], [1, 3], [1, 3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083001,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0002","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],\"subset\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], [[], [1], [1, 3, 4], [1, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 3, 4], [[], [1], [1, 3, 4], [1, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083002,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0003","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],\"subset\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [[], [1], [1, 2], [1, 2, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 4], [[], [1], [1, 2], [1, 2, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083003,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0004","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],\"subset\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [[], [1], [1, 2, 4], [1, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 4], [[], [1], [1, 2, 4], [1, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083004,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0005","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],\"subset\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], [[], [1], [1, 2], [1, 2, 3]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 3], [[], [1], [1, 2], [1, 2, 3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083005,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0006","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],\"subset\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], [[], [1], [1, 2, 3], [1, 3]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 3], [[], [1], [1, 2, 3], [1, 3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083006,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0007","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],\"subset\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], [[], [2], [2, 3], [2, 3, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([2, 3, 4], [[], [2], [2, 3], [2, 3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083007,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0008","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],\"subset\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], [[], [2], [2, 3, 4], [2, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([2, 3, 4], [[], [2], [2, 3, 4], [2, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083008,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0009","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],\"subset\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [[], [1, 2], [1, 2, 4], [2]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 4], [[], [1, 2], [1, 2, 4], [2]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083009,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,2],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0010","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],\"subset\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [[], [1, 2, 4], [2], [2, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 4], [[], [1, 2, 4], [2], [2, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083010,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,2],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0011","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],\"subset\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], [[], [1, 2], [1, 2, 3], [2]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 3], [[], [1, 2], [1, 2, 3], [2]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083011,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0012","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],\"subset\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], [[], [1, 2, 3], [2], [2, 3]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 3], [[], [1, 2, 3], [2], [2, 3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083012,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,2],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0013","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],\"subset\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], [[], [2, 3], [2, 3, 4], [3]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([2, 3, 4], [[], [2, 3], [2, 3, 4], [3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083013,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,3],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0014","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],\"subset\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], [[], [2, 3, 4], [3], [3, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([2, 3, 4], [[], [2, 3, 4], [3], [3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083014,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,3],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0015","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],\"subset\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], [[], [1, 3], [1, 3, 4], [3]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 3, 4], [[], [1, 3], [1, 3, 4], [3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083015,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,3],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0016","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],\"subset\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], [[], [1, 3, 4], [3], [3, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 3, 4], [[], [1, 3, 4], [3], [3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083016,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,3],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0017","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],\"subset\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], [[], [1, 2, 3], [1, 3], [3]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 3], [[], [1, 2, 3], [1, 3], [3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083017,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,3],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0018","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],\"subset\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], [[], [1, 2, 3], [2, 3], [3]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 3], [[], [1, 2, 3], [2, 3], [3]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083018,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0019","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],\"subset\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], [[], [2, 3, 4], [2, 4], [4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([2, 3, 4], [[], [2, 3, 4], [2, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083019,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0020","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],\"subset\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], [[], [2, 3, 4], [3, 4], [4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([2, 3, 4], [[], [2, 3, 4], [3, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083020,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0021","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],\"subset\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], [[], [1, 3, 4], [1, 4], [4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 3, 4], [[], [1, 3, 4], [1, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083021,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0022","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],\"subset\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], [[], [1, 3, 4], [3, 4], [4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 3, 4], [[], [1, 3, 4], [3, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083022,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0023","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],\"subset\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [[], [1, 2, 4], [1, 4], [4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 4], [[], [1, 2, 4], [1, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083023,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0024","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],\"subset\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], [[], [1, 2, 4], [2, 4], [4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([1, 2, 4], [[], [1, 2, 4], [2, 4], [4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083024,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0025","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-induced-topology；資料={\"n\":5,\"parent_topology\":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],\"subset\":[0,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 4], [[], [0], [0, 3], [0, 3, 4]], 4, 是, all_parent_open_intersections_normalized)","explanation_zh":"Wave6第二層核對=([0, 3, 4], [[], [0], [0, 3], [0, 3, 4]], 4, 是, all_parent_open_intersections_normalized)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-induced-topology","seed":202611083025,"parameters":{"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-induced-topology","semantic_template":"qf-mod39-subtop-induced-topology/{\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]],\"subset\":[0,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0026","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3,4],\"candidate\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083026,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4],"candidate":[1],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[1],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0027","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],\"subset\":[1,3,4],\"candidate\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083027,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4],"candidate":[1],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[1],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0028","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],\"subset\":[1,2,4],\"candidate\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], 是, [[0, 1], [0, 1, 3]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083028,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4],"candidate":[1],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[1],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0029","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],\"subset\":[1,2,4],\"candidate\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], 是, [[0, 1], [0, 1, 3]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083029,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4],"candidate":[1],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[1],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0030","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],\"subset\":[1,2,3],\"candidate\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], 是, [[0, 1], [0, 1, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083030,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3],"candidate":[1],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[1],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0031","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],\"subset\":[1,2,3],\"candidate\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], 是, [[0, 1], [0, 1, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([1], 是, [[0, 1], [0, 1, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083031,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3],"candidate":[1],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[1],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0032","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],\"subset\":[2,3,4],\"candidate\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], 是, [[0, 1, 2], [0, 2]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([2], 是, [[0, 1, 2], [0, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083032,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4],"candidate":[2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0033","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],\"subset\":[2,3,4],\"candidate\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], 是, [[0, 1, 2], [0, 2]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([2], 是, [[0, 1, 2], [0, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083033,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4],"candidate":[2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0034","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],\"subset\":[1,2,4],\"candidate\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], 是, [[0, 2], [0, 2, 3]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([2], 是, [[0, 2], [0, 2, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083034,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4],"candidate":[2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,2],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0035","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],\"subset\":[1,2,4],\"candidate\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], 是, [[0, 2], [0, 2, 3]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([2], 是, [[0, 2], [0, 2, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083035,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4],"candidate":[2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,2],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0036","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],\"subset\":[1,2,3],\"candidate\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], 是, [[0, 2], [0, 2, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([2], 是, [[0, 2], [0, 2, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083036,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3],"candidate":[2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0037","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],\"subset\":[1,2,3],\"candidate\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], 是, [[0, 2], [0, 2, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([2], 是, [[0, 2], [0, 2, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083037,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3],"candidate":[2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,2],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0038","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],\"subset\":[2,3,4],\"candidate\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], 是, [[0, 1, 3], [0, 3]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([3], 是, [[0, 1, 3], [0, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083038,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4],"candidate":[3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,3],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0039","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],\"subset\":[2,3,4],\"candidate\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], 是, [[0, 1, 3], [0, 3]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([3], 是, [[0, 1, 3], [0, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083039,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4],"candidate":[3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,3],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0040","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],\"subset\":[1,3,4],\"candidate\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], 是, [[0, 2, 3], [0, 3]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([3], 是, [[0, 2, 3], [0, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083040,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4],"candidate":[3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,3],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0041","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],\"subset\":[1,3,4],\"candidate\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], 是, [[0, 2, 3], [0, 3]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([3], 是, [[0, 2, 3], [0, 3]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083041,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4],"candidate":[3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,3],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0042","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],\"subset\":[1,2,3],\"candidate\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], 是, [[0, 3], [0, 3, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([3], 是, [[0, 3], [0, 3, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083042,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,3],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0043","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],\"subset\":[1,2,3],\"candidate\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], 是, [[0, 3], [0, 3, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([3], 是, [[0, 3], [0, 3, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083043,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0044","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],\"subset\":[2,3,4],\"candidate\":[4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([4], 是, [[0, 1, 4], [0, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([4], 是, [[0, 1, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083044,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0045","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],\"subset\":[2,3,4],\"candidate\":[4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([4], 是, [[0, 1, 4], [0, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([4], 是, [[0, 1, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083045,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0046","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],\"subset\":[1,3,4],\"candidate\":[4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([4], 是, [[0, 2, 4], [0, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([4], 是, [[0, 2, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083046,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0047","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],\"subset\":[1,3,4],\"candidate\":[4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([4], 是, [[0, 2, 4], [0, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([4], 是, [[0, 2, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083047,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0048","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],\"subset\":[1,2,4],\"candidate\":[4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([4], 是, [[0, 3, 4], [0, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([4], 是, [[0, 3, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083048,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0049","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],\"subset\":[1,2,4],\"candidate\":[4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([4], 是, [[0, 3, 4], [0, 4]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([4], 是, [[0, 3, 4], [0, 4]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083049,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0050","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-open-audit；資料={\"n\":5,\"parent_topology\":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],\"subset\":[0,3,4],\"candidate\":[0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)","explanation_zh":"Wave6第二層核對=([0], 是, [[0, 1], [0, 1, 2]], relative_open_need_not_be_ambient_open)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-open-audit","seed":202611083050,"parameters":{"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4],"candidate":[0],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-open-audit","semantic_template":"qf-mod39-subtop-relative-open-audit/{\"candidate\":[0],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]],\"subset\":[0,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0051","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3,4],\"candidate\":[3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [1], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([3, 4], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083051,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4],"candidate":[3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0052","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],\"subset\":[1,3,4],\"candidate\":[3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [1], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([3, 4], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083052,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4],"candidate":[3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0053","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],\"subset\":[1,2,4],\"candidate\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [1], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([2, 4], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083053,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4],"candidate":[2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0054","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],\"subset\":[1,2,4],\"candidate\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [1], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([2, 4], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083054,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4],"candidate":[2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0055","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],\"subset\":[1,2,3],\"candidate\":[2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([2, 3], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083055,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3],"candidate":[2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0056","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],\"subset\":[1,2,3],\"candidate\":[2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([2, 3], [1], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083056,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3],"candidate":[2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0057","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],\"subset\":[2,3,4],\"candidate\":[3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [2], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([3, 4], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083057,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4],"candidate":[3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0058","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],\"subset\":[2,3,4],\"candidate\":[3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [2], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([3, 4], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083058,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4],"candidate":[3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0059","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],\"subset\":[1,2,4],\"candidate\":[1,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [2], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 4], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083059,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4],"candidate":[1,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,2],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0060","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],\"subset\":[1,2,4],\"candidate\":[1,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [2], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 4], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083060,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4],"candidate":[1,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,2],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0061","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],\"subset\":[1,2,3],\"candidate\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [2], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 3], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083061,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3],"candidate":[1,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0062","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],\"subset\":[1,2,3],\"candidate\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [2], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 3], [2], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083062,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3],"candidate":[1,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,2],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0063","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],\"subset\":[2,3,4],\"candidate\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [3], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([2, 4], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083063,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4],"candidate":[2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,3],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0064","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],\"subset\":[2,3,4],\"candidate\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 4], [3], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([2, 4], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083064,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4],"candidate":[2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,3],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0065","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],\"subset\":[1,3,4],\"candidate\":[1,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [3], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 4], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083065,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4],"candidate":[1,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,3],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0066","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],\"subset\":[1,3,4],\"candidate\":[1,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 4], [3], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 4], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083066,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4],"candidate":[1,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,3],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0067","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],\"subset\":[1,2,3],\"candidate\":[1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [3], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 2], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083067,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[1,2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,3],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0068","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],\"subset\":[1,2,3],\"candidate\":[1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [3], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 2], [3], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083068,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[1,2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0069","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],\"subset\":[2,3,4],\"candidate\":[2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [4], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([2, 3], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083069,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0070","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],\"subset\":[2,3,4],\"candidate\":[2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [4], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([2, 3], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083070,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0071","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],\"subset\":[1,3,4],\"candidate\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [4], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 3], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083071,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[1,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0072","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],\"subset\":[1,3,4],\"candidate\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [4], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 3], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083072,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[1,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0073","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],\"subset\":[1,2,4],\"candidate\":[1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [4], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 2], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083073,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[1,2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0074","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],\"subset\":[1,2,4],\"candidate\":[1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2], [4], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([1, 2], [4], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083074,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[1,2],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[1,2],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0075","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-relative-closed-audit；資料={\"n\":5,\"parent_topology\":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],\"subset\":[0,3,4],\"candidate\":[3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3, 4], [0], 是, complement_taken_inside_Y)","explanation_zh":"Wave6第二層核對=([3, 4], [0], 是, complement_taken_inside_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-relative-closed-audit","seed":202611083075,"parameters":{"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4],"candidate":[3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-relative-closed-audit","semantic_template":"qf-mod39-subtop-relative-closed-audit/{\"candidate\":[3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]],\"subset\":[0,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0076","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],\"subset\":[1,3,4],\"candidate\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083076,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4],"candidate":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0077","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],\"subset\":[1,3,4],\"candidate\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083077,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4],"candidate":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0078","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],\"subset\":[1,2,4],\"candidate\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083078,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4],"candidate":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0079","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],\"subset\":[1,2,4],\"candidate\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083079,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4],"candidate":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0080","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],\"subset\":[1,2,3],\"candidate\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083080,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3],"candidate":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0081","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],\"subset\":[1,2,3],\"candidate\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083081,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3],"candidate":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0082","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],\"subset\":[2,3,4],\"candidate\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083082,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4],"candidate":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[2,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0083","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],\"subset\":[2,3,4],\"candidate\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083083,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4],"candidate":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[2,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0084","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],\"subset\":[1,2,4],\"candidate\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083084,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4],"candidate":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,2],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0085","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],\"subset\":[1,2,4],\"candidate\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083085,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4],"candidate":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,2],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0086","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],\"subset\":[1,2,3],\"candidate\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083086,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3],"candidate":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0087","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],\"subset\":[1,2,3],\"candidate\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083087,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3],"candidate":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,2],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0088","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],\"subset\":[2,3,4],\"candidate\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083088,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4],"candidate":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[2,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,3],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0089","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],\"subset\":[2,3,4],\"candidate\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083089,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4],"candidate":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[2,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,3],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0090","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],\"subset\":[1,3,4],\"candidate\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083090,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4],"candidate":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,3],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0091","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],\"subset\":[1,3,4],\"candidate\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083091,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4],"candidate":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,3],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0092","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],\"subset\":[1,2,3],\"candidate\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083092,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,3],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0093","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],\"subset\":[1,2,3],\"candidate\":[1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 3], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083093,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"candidate":[1,2,3],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,3],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]],\"subset\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0094","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],\"subset\":[2,3,4],\"candidate\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083094,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[2,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0095","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],\"subset\":[2,3,4],\"candidate\":[2,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([2, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083095,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4],"candidate":[2,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[2,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]],\"subset\":[2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0096","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],\"subset\":[1,3,4],\"candidate\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083096,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0097","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],\"subset\":[1,3,4],\"candidate\":[1,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083097,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4],"candidate":[1,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]],\"subset\":[1,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0098","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],\"subset\":[1,2,4],\"candidate\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083098,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0099","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],\"subset\":[1,2,4],\"candidate\":[1,2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([1, 2, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083099,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"candidate":[1,2,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[1,2,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]],\"subset\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261108-r03-subspace-topology-0100","batch_id":"batch-20261014-advance-20261108-r03-subspace-topology-foundations","language":"zh-Hant","source_mko_ids":["mko-subspace-topology"],"title_zh":"子空間拓撲","stem_zh":"完整有限母拓撲、明示Y subset X與相對全集Y。操作=subtop-ambient-boundary；資料={\"n\":5,\"parent_topology\":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],\"subset\":[0,3,4],\"candidate\":[0,3,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)","explanation_zh":"Wave6第二層核對=([0, 3, 4], 是, 否, 是, O_intersect_Y_not_O_subset_Y)；依完整明示資料獨立重算；tau_Y恰為全部U intersect Y；relative open不必ambient open且不要求U subset Y；relative closed以Y內補集或F intersect Y判定；重複與空交集須正規化。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子空間拓撲"]},"variant":{"family_id":"qf-mod39-subtop-ambient-boundary","seed":202611083100,"parameters":{"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4],"candidate":[0,3,4],"domain":"Complete_finite_subspace_topology","operation":"subtop-ambient-boundary","semantic_template":"qf-mod39-subtop-ambient-boundary/{\"candidate\":[0,3,4],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]],\"subset\":[0,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、single-step orbit、finite-prefix monotonicity、ambient-relative topology混同、Chebyshev equality、pairwise-only容斥、無Euclid-lemma uniqueness、loopful digraph、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}