{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0001","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":1,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(1, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283001,"parameters":{"dimension":1,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":1,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0002","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":2,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(2, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283002,"parameters":{"dimension":2,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":2,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0003","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":3,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(3, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283003,"parameters":{"dimension":3,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":3,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0004","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":4,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(4, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283004,"parameters":{"dimension":4,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":4,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0005","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":5,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(5, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283005,"parameters":{"dimension":5,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":5,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0006","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":6,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(6, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(6, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283006,"parameters":{"dimension":6,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":6,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0007","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":7,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(7, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(7, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283007,"parameters":{"dimension":7,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":7,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0008","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":8,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(8, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(8, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283008,"parameters":{"dimension":8,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":8,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0009","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":9,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(9, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(9, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283009,"parameters":{"dimension":9,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":9,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0010","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":10,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(10, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(10, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283010,"parameters":{"dimension":10,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":10,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0011","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":11,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(11, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(11, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283011,"parameters":{"dimension":11,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":11,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0012","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":12,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(12, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(12, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283012,"parameters":{"dimension":12,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":12,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0013","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":13,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(13, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(13, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283013,"parameters":{"dimension":13,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":13,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0014","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":14,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(14, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(14, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283014,"parameters":{"dimension":14,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":14,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0015","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":15,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(15, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(15, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283015,"parameters":{"dimension":15,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":15,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0016","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":16,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(16, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(16, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283016,"parameters":{"dimension":16,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":16,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0017","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":17,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(17, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(17, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283017,"parameters":{"dimension":17,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":17,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0018","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":18,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(18, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(18, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283018,"parameters":{"dimension":18,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":18,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0019","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":19,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(19, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(19, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283019,"parameters":{"dimension":19,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":19,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0020","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":20,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(20, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(20, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283020,"parameters":{"dimension":20,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":20,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0021","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":21,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(21, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(21, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283021,"parameters":{"dimension":21,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":21,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0022","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":22,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(22, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(22, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283022,"parameters":{"dimension":22,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":22,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0023","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":23,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(23, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(23, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283023,"parameters":{"dimension":23,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":23,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0024","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":24,\"norm_name\":\"linfinity\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(24, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(24, linfinity, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283024,"parameters":{"dimension":24,"norm_name":"linfinity","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":24,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0025","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-named-certificate；資料={\"dimension\":25,\"norm_name\":\"l1\"}。請依 [dimension,norm_name,carrier,metric_binding,completeness_certificate,Banach,boundary] 欄序回答。","answer":{"kind":"expression","value":"(25, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)","explanation_zh":"Wave4第二層核對=(25, l1, R^n, same_norm_induced_metric, finite_dimensional_real_normed_space_complete, 是, not_Hilbert_claim)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-named-certificate","seed":202610283025,"parameters":{"dimension":25,"norm_name":"l1","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-named-certificate","semantic_template":"qf-mod28-banach-named-certificate/{\"dimension\":25,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0026","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":1,\"norm_name\":\"l1\",\"metric_source\":\"unrelated_metric\",\"completeness_source\":\"sampled_sequences\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(1, l1, unrelated_metric, sampled_sequences, 否, 否, 否)","explanation_zh":"Wave4第二層核對=(1, l1, unrelated_metric, sampled_sequences, 否, 否, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283026,"parameters":{"dimension":1,"norm_name":"l1","metric_source":"unrelated_metric","completeness_source":"sampled_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"sampled_sequences\",\"dimension\":1,\"metric_source\":\"unrelated_metric\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0027","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":2,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(2, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(2, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283027,"parameters":{"dimension":2,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":2,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0028","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":3,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(3, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(3, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283028,"parameters":{"dimension":3,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":3,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0029","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":4,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(4, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(4, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283029,"parameters":{"dimension":4,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":4,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0030","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":5,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"sampled_sequences\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(5, l1, same_norm_induced, sampled_sequences, 是, 否, 否)","explanation_zh":"Wave4第二層核對=(5, l1, same_norm_induced, sampled_sequences, 是, 否, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283030,"parameters":{"dimension":5,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"sampled_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"sampled_sequences\",\"dimension\":5,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0031","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":6,\"norm_name\":\"linfinity\",\"metric_source\":\"unrelated_metric\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(6, linfinity, unrelated_metric, finite_dimensional_theorem, 否, 是, 否)","explanation_zh":"Wave4第二層核對=(6, linfinity, unrelated_metric, finite_dimensional_theorem, 否, 是, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283031,"parameters":{"dimension":6,"norm_name":"linfinity","metric_source":"unrelated_metric","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":6,\"metric_source\":\"unrelated_metric\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0032","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":7,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(7, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(7, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283032,"parameters":{"dimension":7,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":7,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0033","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":8,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(8, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(8, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283033,"parameters":{"dimension":8,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":8,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0034","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":9,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"sampled_sequences\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(9, l1, same_norm_induced, sampled_sequences, 是, 否, 否)","explanation_zh":"Wave4第二層核對=(9, l1, same_norm_induced, sampled_sequences, 是, 否, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283034,"parameters":{"dimension":9,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"sampled_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"sampled_sequences\",\"dimension\":9,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0035","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":10,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(10, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(10, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283035,"parameters":{"dimension":10,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":10,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0036","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":11,\"norm_name\":\"l1\",\"metric_source\":\"unrelated_metric\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(11, l1, unrelated_metric, finite_dimensional_theorem, 否, 是, 否)","explanation_zh":"Wave4第二層核對=(11, l1, unrelated_metric, finite_dimensional_theorem, 否, 是, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283036,"parameters":{"dimension":11,"norm_name":"l1","metric_source":"unrelated_metric","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":11,\"metric_source\":\"unrelated_metric\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0037","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":12,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(12, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(12, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283037,"parameters":{"dimension":12,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":12,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0038","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":13,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"sampled_sequences\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(13, l1, same_norm_induced, sampled_sequences, 是, 否, 否)","explanation_zh":"Wave4第二層核對=(13, l1, same_norm_induced, sampled_sequences, 是, 否, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283038,"parameters":{"dimension":13,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"sampled_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"sampled_sequences\",\"dimension\":13,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0039","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":14,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(14, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(14, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283039,"parameters":{"dimension":14,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":14,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0040","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":15,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(15, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(15, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283040,"parameters":{"dimension":15,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":15,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0041","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":16,\"norm_name\":\"linfinity\",\"metric_source\":\"unrelated_metric\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(16, linfinity, unrelated_metric, finite_dimensional_theorem, 否, 是, 否)","explanation_zh":"Wave4第二層核對=(16, linfinity, unrelated_metric, finite_dimensional_theorem, 否, 是, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283041,"parameters":{"dimension":16,"norm_name":"linfinity","metric_source":"unrelated_metric","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":16,\"metric_source\":\"unrelated_metric\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0042","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":17,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"sampled_sequences\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(17, l1, same_norm_induced, sampled_sequences, 是, 否, 否)","explanation_zh":"Wave4第二層核對=(17, l1, same_norm_induced, sampled_sequences, 是, 否, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283042,"parameters":{"dimension":17,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"sampled_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"sampled_sequences\",\"dimension\":17,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0043","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":18,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(18, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(18, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283043,"parameters":{"dimension":18,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":18,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0044","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":19,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(19, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(19, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283044,"parameters":{"dimension":19,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":19,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0045","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":20,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(20, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(20, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283045,"parameters":{"dimension":20,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":20,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0046","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":21,\"norm_name\":\"l1\",\"metric_source\":\"unrelated_metric\",\"completeness_source\":\"sampled_sequences\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(21, l1, unrelated_metric, sampled_sequences, 否, 否, 否)","explanation_zh":"Wave4第二層核對=(21, l1, unrelated_metric, sampled_sequences, 否, 否, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283046,"parameters":{"dimension":21,"norm_name":"l1","metric_source":"unrelated_metric","completeness_source":"sampled_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"sampled_sequences\",\"dimension\":21,\"metric_source\":\"unrelated_metric\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0047","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":22,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(22, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(22, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283047,"parameters":{"dimension":22,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":22,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0048","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":23,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(23, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(23, l1, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283048,"parameters":{"dimension":23,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":23,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0049","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":24,\"norm_name\":\"linfinity\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(24, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)","explanation_zh":"Wave4第二層核對=(24, linfinity, same_norm_induced, finite_dimensional_theorem, 是, 是, 是)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283049,"parameters":{"dimension":24,"norm_name":"linfinity","metric_source":"same_norm_induced","completeness_source":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"finite_dimensional_theorem\",\"dimension\":24,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0050","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-component-checklist；資料={\"dimension\":25,\"norm_name\":\"l1\",\"metric_source\":\"same_norm_induced\",\"completeness_source\":\"sampled_sequences\"}。請依 [dimension,norm_name,metric_source,completeness_source,metric_same,complete,Banach] 欄序回答。","answer":{"kind":"expression","value":"(25, l1, same_norm_induced, sampled_sequences, 是, 否, 否)","explanation_zh":"Wave4第二層核對=(25, l1, same_norm_induced, sampled_sequences, 是, 否, 否)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-component-checklist","seed":202610283050,"parameters":{"dimension":25,"norm_name":"l1","metric_source":"same_norm_induced","completeness_source":"sampled_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-component-checklist","semantic_template":"qf-mod28-banach-component-checklist/{\"completeness_source\":\"sampled_sequences\",\"dimension\":25,\"metric_source\":\"same_norm_induced\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0051","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[-12,-3,-5],\"right\":[12,-6,-2]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-12, -3, -5], [12, -6, -2], [-24, 3, -3], 30, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [-12, -3, -5], [12, -6, -2], [-24, 3, -3], 30, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283051,"parameters":{"norm_name":"l1","left":[-12,-3,-5],"right":[12,-6,-2],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-12,-3,-5],\"norm_name\":\"l1\",\"right\":[12,-6,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0052","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[-11,-2,-2],\"right\":[11,-1,-1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-11, -2, -2], [11, -1, -1], [-22, -1, -1], 22, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [-11, -2, -2], [11, -1, -1], [-22, -1, -1], 22, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283052,"parameters":{"norm_name":"linfinity","left":[-11,-2,-2],"right":[11,-1,-1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-11,-2,-2],\"norm_name\":\"linfinity\",\"right\":[11,-1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0053","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[-10,-1,1],\"right\":[10,4,0]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-10, -1, 1], [10, 4, 0], [-20, -5, 1], 26, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [-10, -1, 1], [10, 4, 0], [-20, -5, 1], 26, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283053,"parameters":{"norm_name":"l1","left":[-10,-1,1],"right":[10,4,0],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-10,-1,1],\"norm_name\":\"l1\",\"right\":[10,4,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0054","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[-9,0,4],\"right\":[9,-4,1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-9, 0, 4], [9, -4, 1], [-18, 4, 3], 18, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [-9, 0, 4], [9, -4, 1], [-18, 4, 3], 18, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283054,"parameters":{"norm_name":"linfinity","left":[-9,0,4],"right":[9,-4,1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-9,0,4],\"norm_name\":\"linfinity\",\"right\":[9,-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0055","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[-8,1,-4],\"right\":[8,1,-2]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-8, 1, -4], [8, 1, -2], [-16, 0, -2], 18, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [-8, 1, -4], [8, 1, -2], [-16, 0, -2], 18, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283055,"parameters":{"norm_name":"l1","left":[-8,1,-4],"right":[8,1,-2],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-8,1,-4],\"norm_name\":\"l1\",\"right\":[8,1,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0056","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[-7,2,-1],\"right\":[7,6,-1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-7, 2, -1], [7, 6, -1], [-14, -4, 0], 14, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [-7, 2, -1], [7, 6, -1], [-14, -4, 0], 14, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283056,"parameters":{"norm_name":"linfinity","left":[-7,2,-1],"right":[7,6,-1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-7,2,-1],\"norm_name\":\"linfinity\",\"right\":[7,6,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0057","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[-6,3,2],\"right\":[6,-2,0]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-6, 3, 2], [6, -2, 0], [-12, 5, 2], 19, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [-6, 3, 2], [6, -2, 0], [-12, 5, 2], 19, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283057,"parameters":{"norm_name":"l1","left":[-6,3,2],"right":[6,-2,0],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-6,3,2],\"norm_name\":\"l1\",\"right\":[6,-2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0058","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[-5,-3,5],\"right\":[5,3,1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-5, -3, 5], [5, 3, 1], [-10, -6, 4], 10, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [-5, -3, 5], [5, 3, 1], [-10, -6, 4], 10, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283058,"parameters":{"norm_name":"linfinity","left":[-5,-3,5],"right":[5,3,1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-5,-3,5],\"norm_name\":\"linfinity\",\"right\":[5,3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0059","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[-4,-2,-3],\"right\":[4,-5,-2]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-4, -2, -3], [4, -5, -2], [-8, 3, -1], 12, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [-4, -2, -3], [4, -5, -2], [-8, 3, -1], 12, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283059,"parameters":{"norm_name":"l1","left":[-4,-2,-3],"right":[4,-5,-2],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-4,-2,-3],\"norm_name\":\"l1\",\"right\":[4,-5,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0060","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[-3,-1,0],\"right\":[3,0,-1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-3, -1, 0], [3, 0, -1], [-6, -1, 1], 6, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [-3, -1, 0], [3, 0, -1], [-6, -1, 1], 6, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283060,"parameters":{"norm_name":"linfinity","left":[-3,-1,0],"right":[3,0,-1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-3,-1,0],\"norm_name\":\"linfinity\",\"right\":[3,0,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0061","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[-2,0,3],\"right\":[2,5,0]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-2, 0, 3], [2, 5, 0], [-4, -5, 3], 12, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [-2, 0, 3], [2, 5, 0], [-4, -5, 3], 12, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283061,"parameters":{"norm_name":"l1","left":[-2,0,3],"right":[2,5,0],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-2,0,3],\"norm_name\":\"l1\",\"right\":[2,5,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0062","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[-1,1,-5],\"right\":[1,-3,1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-1, 1, -5], [1, -3, 1], [-2, 4, -6], 6, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [-1, 1, -5], [1, -3, 1], [-2, 4, -6], 6, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283062,"parameters":{"norm_name":"linfinity","left":[-1,1,-5],"right":[1,-3,1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[-1,1,-5],\"norm_name\":\"linfinity\",\"right\":[1,-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0063","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[0,2,-2],\"right\":[0,2,-2]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [0, 2, -2], [0, 2, -2], [0, 0, 0], 0, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [0, 2, -2], [0, 2, -2], [0, 0, 0], 0, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283063,"parameters":{"norm_name":"l1","left":[0,2,-2],"right":[0,2,-2],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[0,2,-2],\"norm_name\":\"l1\",\"right\":[0,2,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0064","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[1,3,1],\"right\":[-1,-6,-1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [1, 3, 1], [-1, -6, -1], [2, 9, 2], 9, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [1, 3, 1], [-1, -6, -1], [2, 9, 2], 9, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283064,"parameters":{"norm_name":"linfinity","left":[1,3,1],"right":[-1,-6,-1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[1,3,1],\"norm_name\":\"linfinity\",\"right\":[-1,-6,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0065","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[2,-3,4],\"right\":[-2,-1,0]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [2, -3, 4], [-2, -1, 0], [4, -2, 4], 10, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [2, -3, 4], [-2, -1, 0], [4, -2, 4], 10, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283065,"parameters":{"norm_name":"l1","left":[2,-3,4],"right":[-2,-1,0],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[2,-3,4],\"norm_name\":\"l1\",\"right\":[-2,-1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0066","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[3,-2,-4],\"right\":[-3,4,1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [3, -2, -4], [-3, 4, 1], [6, -6, -5], 6, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [3, -2, -4], [-3, 4, 1], [6, -6, -5], 6, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283066,"parameters":{"norm_name":"linfinity","left":[3,-2,-4],"right":[-3,4,1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[3,-2,-4],\"norm_name\":\"linfinity\",\"right\":[-3,4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0067","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[4,-1,-1],\"right\":[-4,-4,-2]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [4, -1, -1], [-4, -4, -2], [8, 3, 1], 12, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [4, -1, -1], [-4, -4, -2], [8, 3, 1], 12, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283067,"parameters":{"norm_name":"l1","left":[4,-1,-1],"right":[-4,-4,-2],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[4,-1,-1],\"norm_name\":\"l1\",\"right\":[-4,-4,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0068","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[5,0,2],\"right\":[-5,1,-1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [5, 0, 2], [-5, 1, -1], [10, -1, 3], 10, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [5, 0, 2], [-5, 1, -1], [10, -1, 3], 10, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283068,"parameters":{"norm_name":"linfinity","left":[5,0,2],"right":[-5,1,-1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[5,0,2],\"norm_name\":\"linfinity\",\"right\":[-5,1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0069","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[6,1,5],\"right\":[-6,6,0]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [6, 1, 5], [-6, 6, 0], [12, -5, 5], 22, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [6, 1, 5], [-6, 6, 0], [12, -5, 5], 22, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283069,"parameters":{"norm_name":"l1","left":[6,1,5],"right":[-6,6,0],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[6,1,5],\"norm_name\":\"l1\",\"right\":[-6,6,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0070","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[7,2,-3],\"right\":[-7,-2,1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [7, 2, -3], [-7, -2, 1], [14, 4, -4], 14, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [7, 2, -3], [-7, -2, 1], [14, 4, -4], 14, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283070,"parameters":{"norm_name":"linfinity","left":[7,2,-3],"right":[-7,-2,1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[7,2,-3],\"norm_name\":\"linfinity\",\"right\":[-7,-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0071","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[8,3,0],\"right\":[-8,3,-2]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [8, 3, 0], [-8, 3, -2], [16, 0, 2], 18, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [8, 3, 0], [-8, 3, -2], [16, 0, 2], 18, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283071,"parameters":{"norm_name":"l1","left":[8,3,0],"right":[-8,3,-2],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[8,3,0],\"norm_name\":\"l1\",\"right\":[-8,3,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0072","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[9,-3,3],\"right\":[-9,-5,-1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [9, -3, 3], [-9, -5, -1], [18, 2, 4], 18, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [9, -3, 3], [-9, -5, -1], [18, 2, 4], 18, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283072,"parameters":{"norm_name":"linfinity","left":[9,-3,3],"right":[-9,-5,-1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[9,-3,3],\"norm_name\":\"linfinity\",\"right\":[-9,-5,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0073","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[10,-2,-5],\"right\":[-10,0,0]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [10, -2, -5], [-10, 0, 0], [20, -2, -5], 27, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [10, -2, -5], [-10, 0, 0], [20, -2, -5], 27, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283073,"parameters":{"norm_name":"l1","left":[10,-2,-5],"right":[-10,0,0],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[10,-2,-5],\"norm_name\":\"l1\",\"right\":[-10,0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0074","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"linfinity\",\"left\":[11,-1,-2],\"right\":[-11,5,1]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [11, -1, -2], [-11, 5, 1], [22, -6, -3], 22, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(linfinity, [11, -1, -2], [-11, 5, 1], [22, -6, -3], 22, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283074,"parameters":{"norm_name":"linfinity","left":[11,-1,-2],"right":[-11,5,1],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[11,-1,-2],\"norm_name\":\"linfinity\",\"right\":[-11,5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0075","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-distance-evaluate；資料={\"norm_name\":\"l1\",\"left\":[12,0,1],\"right\":[-12,-3,-2]}。請依 [norm_name,left,right,difference,distance,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [12, 0, 1], [-12, -3, -2], [24, 3, 3], 30, distance_evaluation_not_completeness_proof)","explanation_zh":"Wave4第二層核對=(l1, [12, 0, 1], [-12, -3, -2], [24, 3, 3], 30, distance_evaluation_not_completeness_proof)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-distance-evaluate","seed":202610283075,"parameters":{"norm_name":"l1","left":[12,0,1],"right":[-12,-3,-2],"domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-distance-evaluate","semantic_template":"qf-mod28-banach-distance-evaluate/{\"left\":[12,0,1],\"norm_name\":\"l1\",\"right\":[-12,-3,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0076","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":1,\"norm_name\":\"l1\",\"evidence_mode\":\"sampled_cauchy_sequences\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)","explanation_zh":"Wave4第二層核對=(1, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283076,"parameters":{"dimension":1,"norm_name":"l1","evidence_mode":"sampled_cauchy_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":1,\"evidence_mode\":\"sampled_cauchy_sequences\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0077","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":2,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(2, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283077,"parameters":{"dimension":2,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":2,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0078","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":3,\"norm_name\":\"l1\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, l1, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(3, l1, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283078,"parameters":{"dimension":3,"norm_name":"l1","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":3,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0079","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":4,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(4, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283079,"parameters":{"dimension":4,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":4,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0080","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":5,\"norm_name\":\"l1\",\"evidence_mode\":\"sampled_cauchy_sequences\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)","explanation_zh":"Wave4第二層核對=(5, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283080,"parameters":{"dimension":5,"norm_name":"l1","evidence_mode":"sampled_cauchy_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":5,\"evidence_mode\":\"sampled_cauchy_sequences\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0081","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":6,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(6, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(6, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283081,"parameters":{"dimension":6,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":6,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0082","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":7,\"norm_name\":\"l1\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(7, l1, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(7, l1, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283082,"parameters":{"dimension":7,"norm_name":"l1","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":7,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0083","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":8,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(8, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(8, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283083,"parameters":{"dimension":8,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":8,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0084","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":9,\"norm_name\":\"l1\",\"evidence_mode\":\"sampled_cauchy_sequences\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(9, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)","explanation_zh":"Wave4第二層核對=(9, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283084,"parameters":{"dimension":9,"norm_name":"l1","evidence_mode":"sampled_cauchy_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":9,\"evidence_mode\":\"sampled_cauchy_sequences\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0085","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":10,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(10, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(10, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283085,"parameters":{"dimension":10,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":10,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0086","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":11,\"norm_name\":\"l1\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(11, l1, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(11, l1, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283086,"parameters":{"dimension":11,"norm_name":"l1","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":11,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0087","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":12,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(12, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(12, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283087,"parameters":{"dimension":12,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":12,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0088","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":13,\"norm_name\":\"l1\",\"evidence_mode\":\"sampled_cauchy_sequences\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(13, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)","explanation_zh":"Wave4第二層核對=(13, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283088,"parameters":{"dimension":13,"norm_name":"l1","evidence_mode":"sampled_cauchy_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":13,\"evidence_mode\":\"sampled_cauchy_sequences\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0089","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":14,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(14, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(14, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283089,"parameters":{"dimension":14,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":14,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0090","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":15,\"norm_name\":\"l1\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(15, l1, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(15, l1, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283090,"parameters":{"dimension":15,"norm_name":"l1","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":15,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0091","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":16,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(16, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(16, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283091,"parameters":{"dimension":16,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":16,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0092","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":17,\"norm_name\":\"l1\",\"evidence_mode\":\"sampled_cauchy_sequences\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(17, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)","explanation_zh":"Wave4第二層核對=(17, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283092,"parameters":{"dimension":17,"norm_name":"l1","evidence_mode":"sampled_cauchy_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":17,\"evidence_mode\":\"sampled_cauchy_sequences\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0093","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":18,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(18, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(18, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283093,"parameters":{"dimension":18,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":18,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0094","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":19,\"norm_name\":\"l1\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(19, l1, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(19, l1, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283094,"parameters":{"dimension":19,"norm_name":"l1","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":19,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0095","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":20,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(20, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(20, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283095,"parameters":{"dimension":20,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":20,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0096","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":21,\"norm_name\":\"l1\",\"evidence_mode\":\"sampled_cauchy_sequences\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(21, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)","explanation_zh":"Wave4第二層核對=(21, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283096,"parameters":{"dimension":21,"norm_name":"l1","evidence_mode":"sampled_cauchy_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":21,\"evidence_mode\":\"sampled_cauchy_sequences\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0097","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":22,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(22, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(22, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283097,"parameters":{"dimension":22,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":22,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0098","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":23,\"norm_name\":\"l1\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(23, l1, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(23, l1, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283098,"parameters":{"dimension":23,"norm_name":"l1","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":23,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0099","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":24,\"norm_name\":\"linfinity\",\"evidence_mode\":\"finite_dimensional_theorem\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(24, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)","explanation_zh":"Wave4第二層核對=(24, linfinity, finite_dimensional_theorem, 是, universal_named_certificate)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283099,"parameters":{"dimension":24,"norm_name":"linfinity","evidence_mode":"finite_dimensional_theorem","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":24,\"evidence_mode\":\"finite_dimensional_theorem\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r03-real-banach-space-0100","batch_id":"batch-20261014-advance-20261028-r03-real-banach-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-banach-space"],"title_zh":"實Banach空間","stem_zh":"載體norm誘導metric與完備證書必須描述同一空間。操作=banach-evidence-mode-audit；資料={\"dimension\":25,\"norm_name\":\"l1\",\"evidence_mode\":\"sampled_cauchy_sequences\"}。請依 [dimension,norm_name,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(25, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)","explanation_zh":"Wave4第二層核對=(25, l1, sampled_cauchy_sequences, 否, samples_insufficient_for_completeness)；依完整明示資料重算；完整有限／命名精確切片不自動升格為任意無限定理；有限維實賦範空間使用命名全稱完備定理；抽樣Cauchy序列不足且不推出Hilbert。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實Banach空間"]},"variant":{"family_id":"qf-mod28-banach-evidence-mode-audit","seed":202610283100,"parameters":{"dimension":25,"norm_name":"l1","evidence_mode":"sampled_cauchy_sequences","domain":"Named_finite_dimensional_real_Banach_space","operation":"banach-evidence-mode-audit","semantic_template":"qf-mod28-banach-evidence-mode-audit/{\"dimension\":25,\"evidence_mode\":\"sampled_cauchy_sequences\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、整環／域、Hilbert、無限維算子、mutual independence、有向連通、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}