{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261109-r03-compact-subset-0001","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093001,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0002","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093002,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0003","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093003,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0004","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093004,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0005","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093005,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0006","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093006,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0007","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093007,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0008","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093008,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0009","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093009,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0010","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093010,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0011","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093011,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0012","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093012,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0013","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093013,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0014","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093014,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0015","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093015,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0016","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093016,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0017","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093017,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0018","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093018,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0019","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093019,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0020","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093020,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0021","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093021,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0022","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093022,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0023","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093023,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0024","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093024,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0025","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-finite-compactness；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], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)","explanation_zh":"Wave6第三層核對=([0, 3, 4], 4, 是, 否, every_open_cover_drawn_from_finite_topology_is_finite)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-finite-compactness","seed":202611093025,"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_compact_subspace","operation":"compact-finite-compactness","semantic_template":"qf-mod40-compact-finite-compactness/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0026","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1],[1,3],[1,3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1], [1, 3], [1, 3, 4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1], [1, 3], [1, 3, 4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093026,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4],"cover":[[],[1],[1,3],[1,3,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,3,4],[1,3],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0027","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1],[1,3,4],[1,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1], [1, 3, 4], [1, 4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1], [1, 3, 4], [1, 4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093027,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4],"cover":[[],[1],[1,3,4],[1,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,3,4],[1,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0028","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1],[1,2],[1,2,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1], [1, 2], [1, 2, 4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1], [1, 2], [1, 2, 4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093028,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4],"cover":[[],[1],[1,2],[1,2,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,4],[1,2],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0029","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1],[1,2,4],[1,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1], [1, 2, 4], [1, 4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1], [1, 2, 4], [1, 4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093029,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4],"cover":[[],[1],[1,2,4],[1,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,4],[1,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0030","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1],[1,2],[1,2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1], [1, 2], [1, 2, 3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1], [1, 2], [1, 2, 3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093030,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3],"cover":[[],[1],[1,2],[1,2,3]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,3],[1,2],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0031","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1],[1,2,3],[1,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1], [1, 2, 3], [1, 3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1], [1, 2, 3], [1, 3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093031,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3],"cover":[[],[1],[1,2,3],[1,3]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,3],[1,3],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0032","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[2],[2,3],[2,3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [2], [2, 3], [2, 3, 4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [2], [2, 3], [2, 3, 4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093032,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4],"cover":[[],[2],[2,3],[2,3,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[2,3,4],[2,3],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0033","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[2],[2,3,4],[2,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [2], [2, 3, 4], [2, 4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [2], [2, 3, 4], [2, 4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093033,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4],"cover":[[],[2],[2,3,4],[2,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[2,3,4],[2,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0034","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,2],[1,2,4],[2]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 2], [1, 2, 4], [2]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 2], [1, 2, 4], [2]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093034,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4],"cover":[[],[1,2],[1,2,4],[2]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,4],[1,2],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0035","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,2,4],[2],[2,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 2, 4], [2], [2, 4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 2, 4], [2], [2, 4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093035,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4],"cover":[[],[1,2,4],[2],[2,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,4],[2,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0036","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,2],[1,2,3],[2]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 2], [1, 2, 3], [2]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 2], [1, 2, 3], [2]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093036,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3],"cover":[[],[1,2],[1,2,3],[2]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,3],[1,2],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0037","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,2,3],[2],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 2, 3], [2], [2, 3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 2, 3], [2], [2, 3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093037,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3],"cover":[[],[1,2,3],[2],[2,3]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,3],[2,3],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0038","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[2,3],[2,3,4],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [2, 3], [2, 3, 4], [3]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [2, 3], [2, 3, 4], [3]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093038,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4],"cover":[[],[2,3],[2,3,4],[3]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[2,3,4],[2,3],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0039","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[2,3,4],[3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [2, 3, 4], [3], [3, 4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [2, 3, 4], [3], [3, 4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093039,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4],"cover":[[],[2,3,4],[3],[3,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[2,3,4],[3,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0040","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,3],[1,3,4],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 3], [1, 3, 4], [3]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 3], [1, 3, 4], [3]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093040,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4],"cover":[[],[1,3],[1,3,4],[3]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,3,4],[1,3],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0041","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,3,4],[3],[3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 3, 4], [3], [3, 4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 3, 4], [3], [3, 4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093041,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4],"cover":[[],[1,3,4],[3],[3,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,3,4],[3,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0042","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,2,3],[1,3],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 2, 3], [1, 3], [3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 2, 3], [1, 3], [3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093042,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"cover":[[],[1,2,3],[1,3],[3]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,3],[1,3],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0043","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,2,3],[2,3],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 2, 3], [2, 3], [3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 2, 3], [2, 3], [3]], 是, [1, 2, 3], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093043,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"cover":[[],[1,2,3],[2,3],[3]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,3],[2,3],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0044","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[2,3,4],[2,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [2, 3, 4], [2, 4], [4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [2, 3, 4], [2, 4], [4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093044,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4],"cover":[[],[2,3,4],[2,4],[4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[2,3,4],[2,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0045","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[2,3,4],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [2, 3, 4], [3, 4], [4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [2, 3, 4], [3, 4], [4]], 是, [2, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093045,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4],"cover":[[],[2,3,4],[3,4],[4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[2,3,4],[3,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0046","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,3,4],[1,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 3, 4], [1, 4], [4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 3, 4], [1, 4], [4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093046,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4],"cover":[[],[1,3,4],[1,4],[4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,3,4],[1,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0047","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,3,4],[3,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 3, 4], [3, 4], [4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 3, 4], [3, 4], [4]], 是, [1, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093047,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4],"cover":[[],[1,3,4],[3,4],[4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,3,4],[3,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0048","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,2,4],[1,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 2, 4], [1, 4], [4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 2, 4], [1, 4], [4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093048,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"cover":[[],[1,2,4],[1,4],[4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,4],[1,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0049","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[1,2,4],[2,4],[4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [1, 2, 4], [2, 4], [4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [1, 2, 4], [2, 4], [4]], 是, [1, 2, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093049,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"cover":[[],[1,2,4],[2,4],[4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[1,2,4],[2,4],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0050","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-open-cover-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],\"cover\":[[],[0],[0,3],[0,3,4]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[], [0], [0, 3], [0, 3, 4]], 是, [0, 3, 4], single_cover_audit_not_general_compactness_proof)","explanation_zh":"Wave6第三層核對=([[], [0], [0, 3], [0, 3, 4]], 是, [0, 3, 4], single_cover_audit_not_general_compactness_proof)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-open-cover-audit","seed":202611093050,"parameters":{"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4],"cover":[[],[0],[0,3],[0,3,4]],"domain":"Complete_finite_compact_subspace","operation":"compact-open-cover-audit","semantic_template":"qf-mod40-compact-open-cover-audit/{\"cover\":[[],[0,3,4],[0,3],[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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0051","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1],[1,3],[1,3,4]],\"selected\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([3], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093051,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4]],"subset":[1,3,4],"cover":[[],[1],[1,3],[1,3,4]],"selected":[3],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,3,4],[1,3],[1]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[0]],\"selected\":[3],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0052","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1],[1,3,4],[1,4]],\"selected\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([2], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093052,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2],[0,1,2,3,4],[0,1,2,4]],"subset":[1,3,4],"cover":[[],[1],[1,3,4],[1,4]],"selected":[2],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,3,4],[1,4],[1]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,1],[0]],\"selected\":[2],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0053","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1],[1,2],[1,2,4]],\"selected\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([3], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093053,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3],[0,1,2,3,4],[0,1,3]],"subset":[1,2,4],"cover":[[],[1],[1,2],[1,2,4]],"selected":[3],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,4],[1,2],[1]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,1],[0]],\"selected\":[3],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0054","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1],[1,2,4],[1,4]],\"selected\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([2], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093054,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3],[0,1,3,4]],"subset":[1,2,4],"cover":[[],[1],[1,2,4],[1,4]],"selected":[2],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,4],[1,4],[1]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,1],[0]],\"selected\":[2],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0055","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1],[1,2],[1,2,3]],\"selected\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([3], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093055,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,2,4],[0,1,4]],"subset":[1,2,3],"cover":[[],[1],[1,2],[1,2,3]],"selected":[3],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,3],[1,2],[1]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,1],[0]],\"selected\":[3],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0056","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1],[1,2,3],[1,3]],\"selected\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([2], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093056,"parameters":{"n":5,"parent_topology":[[],[0],[0,1],[0,1,2,3,4],[0,1,3,4],[0,1,4]],"subset":[1,2,3],"cover":[[],[1],[1,2,3],[1,3]],"selected":[2],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,3],[1,3],[1]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,1],[0]],\"selected\":[2],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0057","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[2],[2,3],[2,3,4]],\"selected\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([3], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093057,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3],[0,1,2,3,4],[0,2]],"subset":[2,3,4],"cover":[[],[2],[2,3],[2,3,4]],"selected":[3],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[2,3,4],[2,3],[2]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,2],[0]],\"selected\":[3],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0058","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[2],[2,3,4],[2,4]],\"selected\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([2], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093058,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2],[0,1,2,3,4],[0,1,2,4],[0,2]],"subset":[2,3,4],"cover":[[],[2],[2,3,4],[2,4]],"selected":[2],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[2,3,4],[2,4],[2]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,2],[0,2],[0]],\"selected\":[2],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0059","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,2],[1,2,4],[2]],\"selected\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([2], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093059,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2],[0,2,3]],"subset":[1,2,4],"cover":[[],[1,2],[1,2,4],[2]],"selected":[2],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,4],[1,2],[2]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,2],[0]],\"selected\":[2],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0060","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,2,4],[2],[2,4]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093060,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3],[0,2,3,4]],"subset":[1,2,4],"cover":[[],[1,2,4],[2],[2,4]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,4],[2,4],[2]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,2],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0061","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,2],[1,2,3],[2]],\"selected\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([2], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093061,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2],[0,2,4]],"subset":[1,2,3],"cover":[[],[1,2],[1,2,3],[2]],"selected":[2],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,3],[1,2],[2]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,2],[0]],\"selected\":[2],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0062","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,2,3],[2],[2,3]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093062,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2],[0,2,3,4],[0,2,4]],"subset":[1,2,3],"cover":[[],[1,2,3],[2],[2,3]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,3],[2,3],[2]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,2],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0063","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[2,3],[2,3,4],[3]],\"selected\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([2], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093063,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,1,3],[0,3]],"subset":[2,3,4],"cover":[[],[2,3],[2,3,4],[3]],"selected":[2],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[2,3,4],[2,3],[3]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,3],[0,3],[0]],\"selected\":[2],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0064","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[2,3,4],[3],[3,4]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093064,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3],[0,1,3,4],[0,3]],"subset":[2,3,4],"cover":[[],[2,3,4],[3],[3,4]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[2,3,4],[3,4],[3]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,3],[0,3],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0065","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,3],[1,3,4],[3]],\"selected\":[2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([2], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093065,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3],[0,1,2,3,4],[0,2,3],[0,3]],"subset":[1,3,4],"cover":[[],[1,3],[1,3,4],[3]],"selected":[2],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,3,4],[1,3],[3]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,2,3],[0,3],[0]],\"selected\":[2],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0066","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,3,4],[3],[3,4]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093066,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3],[0,2,3,4],[0,3]],"subset":[1,3,4],"cover":[[],[1,3,4],[3],[3,4]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,3,4],[3,4],[3]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,3],[0,3],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0067","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,2,3],[1,3],[3]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093067,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"cover":[[],[1,2,3],[1,3],[3]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,3],[1,3],[3]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,3],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0068","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,2,3],[2,3],[3]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[1, 2, 3]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093068,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3],[0,3,4]],"subset":[1,2,3],"cover":[[],[1,2,3],[2,3],[3]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,3],[2,3],[3]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,3],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0069","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[2,3,4],[2,4],[4]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093069,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4]],"subset":[2,3,4],"cover":[[],[2,3,4],[2,4],[4]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[2,3,4],[2,4],[4]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,1,4],[0,4],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0070","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[2,3,4],[3,4],[4]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[2, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093070,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4]],"subset":[2,3,4],"cover":[[],[2,3,4],[3,4],[4]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[2,3,4],[3,4],[4]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,1,4],[0,4],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0071","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,3,4],[1,4],[4]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093071,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4]],"subset":[1,3,4],"cover":[[],[1,3,4],[1,4],[4]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,3,4],[1,4],[4]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,4],[0,2,4],[0,4],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0072","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,3,4],[3,4],[4]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[1, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093072,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4]],"subset":[1,3,4],"cover":[[],[1,3,4],[3,4],[4]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,3,4],[3,4],[4]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,2,4],[0,4],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0073","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,2,4],[1,4],[4]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093073,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"cover":[[],[1,2,4],[1,4],[4]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,4],[1,4],[4]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,3,4],[0,3,4],[0,4],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0074","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[1,2,4],[2,4],[4]],\"selected\":[1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([1], [[1, 2, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093074,"parameters":{"n":5,"parent_topology":[[],[0],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4]],"subset":[1,2,4],"cover":[[],[1,2,4],[2,4],[4]],"selected":[1],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[1,2,4],[2,4],[4]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,2,3,4],[0,3,4],[0,4],[0]],\"selected\":[1],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0075","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-subcover-certificate；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],\"cover\":[[],[0],[0,3],[0,3,4]],\"selected\":[3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3], [[0, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)","explanation_zh":"Wave6第三層核對=([3], [[0, 3, 4]], 是, 是, finite_subcover_selected_only_from_original_cover)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-subcover-certificate","seed":202611093075,"parameters":{"n":5,"parent_topology":[[],[0,1],[0,1,2],[0,1,2,3],[0,1,2,3,4],[1]],"subset":[0,3,4],"cover":[[],[0],[0,3],[0,3,4]],"selected":[3],"domain":"Complete_finite_compact_subspace","operation":"compact-subcover-certificate","semantic_template":"qf-mod40-compact-subcover-certificate/{\"cover\":[[],[0,3,4],[0,3],[0]],\"n\":5,\"parent_topology\":[[],[0,1,2,3,4],[0,1,2,3],[0,1,2],[0,1],[1]],\"selected\":[3],\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0076","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093076,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0077","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093077,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0078","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093078,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0079","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093079,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0080","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093080,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0081","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093081,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0082","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093082,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0083","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093083,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0084","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093084,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0085","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093085,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0086","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093086,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0087","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093087,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0088","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093088,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0089","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093089,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0090","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093090,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0091","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093091,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0092","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093092,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0093","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 3], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093093,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0094","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093094,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0095","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([2, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093095,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0096","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093096,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0097","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093097,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0098","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093098,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0099","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([1, 2, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093099,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、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-20261109-r03-compact-subset-0100","batch_id":"batch-20261014-advance-20261109-r03-compact-subset-foundations","language":"zh-Hant","source_mko_ids":["mko-compact-subset"],"title_zh":"緊緻子集","stem_zh":"完整有限subspace topology與relative open covers。操作=compact-nonproperty-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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)","explanation_zh":"Wave6第三層核對=([0, 3, 4], 是, 否, 否, compact_does_not_generally_imply_ambient_closed_or_bounded_without_extra_structure)；依完整明示資料獨立重算；cover必須覆蓋K且subcover只能選自original cover；single cover不證一般compactness；finite-space compactness不外推infinite spaces；不把compact普遍當closed-and-bounded，empty set convention明示。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["緊緻子集"]},"variant":{"family_id":"qf-mod40-compact-nonproperty-boundary","seed":202611093100,"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_compact_subspace","operation":"compact-nonproperty-boundary","semantic_template":"qf-mod40-compact-nonproperty-boundary/{\"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-element stabilizer、finite-prefix BW、single-cover compactness、zero-mass division、noncommutative binomial、incomplete Möbius factorization、bounded-search nonmembership、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}