{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261028-r05-bounded-linear-operator-0001","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-12,-3,-5],[-2,12,-6]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-12, -3, -5], [-2, 12, -6]], [14, 15, 11], 15, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-12, -3, -5], [-2, 12, -6]], [14, 15, 11], 15, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285001,"parameters":{"matrix":[[-12,-3,-5],[-2,12,-6]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-12,-3,-5],[-2,12,-6]]}"}},"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-r05-bounded-linear-operator-0002","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-11,-2,-2],[-1,11,-1]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-11, -2, -2], [-1, 11, -1]], [12, 13, 3], 13, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-11, -2, -2], [-1, 11, -1]], [12, 13, 3], 13, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285002,"parameters":{"matrix":[[-11,-2,-2],[-1,11,-1]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-11,-2,-2],[-1,11,-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-r05-bounded-linear-operator-0003","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-10,-1,1],[0,10,4]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-10, -1, 1], [0, 10, 4]], [10, 11, 5], 11, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-10, -1, 1], [0, 10, 4]], [10, 11, 5], 11, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285003,"parameters":{"matrix":[[-10,-1,1],[0,10,4]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-10,-1,1],[0,10,4]]}"}},"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-r05-bounded-linear-operator-0004","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-9,0,4],[1,9,-4]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-9, 0, 4], [1, 9, -4]], [10, 9, 8], 10, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-9, 0, 4], [1, 9, -4]], [10, 9, 8], 10, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285004,"parameters":{"matrix":[[-9,0,4],[1,9,-4]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-9,0,4],[1,9,-4]]}"}},"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-r05-bounded-linear-operator-0005","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-8,1,-4],[2,8,1]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-8, 1, -4], [2, 8, 1]], [10, 9, 5], 10, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-8, 1, -4], [2, 8, 1]], [10, 9, 5], 10, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285005,"parameters":{"matrix":[[-8,1,-4],[2,8,1]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-8,1,-4],[2,8,1]]}"}},"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-r05-bounded-linear-operator-0006","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-7,2,-1],[-2,7,6]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-7, 2, -1], [-2, 7, 6]], [9, 9, 7], 9, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-7, 2, -1], [-2, 7, 6]], [9, 9, 7], 9, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285006,"parameters":{"matrix":[[-7,2,-1],[-2,7,6]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-7,2,-1],[-2,7,6]]}"}},"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-r05-bounded-linear-operator-0007","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-6,3,2],[-1,6,-2]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-6, 3, 2], [-1, 6, -2]], [7, 9, 4], 9, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-6, 3, 2], [-1, 6, -2]], [7, 9, 4], 9, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285007,"parameters":{"matrix":[[-6,3,2],[-1,6,-2]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-6,3,2],[-1,6,-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-r05-bounded-linear-operator-0008","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-5,-3,5],[0,5,3]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-5, -3, 5], [0, 5, 3]], [5, 8, 8], 8, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-5, -3, 5], [0, 5, 3]], [5, 8, 8], 8, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285008,"parameters":{"matrix":[[-5,-3,5],[0,5,3]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-5,-3,5],[0,5,3]]}"}},"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-r05-bounded-linear-operator-0009","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-4,-2,-3],[1,4,-5]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-4, -2, -3], [1, 4, -5]], [5, 6, 8], 8, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-4, -2, -3], [1, 4, -5]], [5, 6, 8], 8, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285009,"parameters":{"matrix":[[-4,-2,-3],[1,4,-5]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-4,-2,-3],[1,4,-5]]}"}},"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-r05-bounded-linear-operator-0010","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-3,-1,0],[2,3,0]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-3, -1, 0], [2, 3, 0]], [5, 4, 0], 5, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-3, -1, 0], [2, 3, 0]], [5, 4, 0], 5, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285010,"parameters":{"matrix":[[-3,-1,0],[2,3,0]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-3,-1,0],[2,3,0]]}"}},"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-r05-bounded-linear-operator-0011","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-2,0,3],[-2,2,5]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-2, 0, 3], [-2, 2, 5]], [4, 2, 8], 8, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-2, 0, 3], [-2, 2, 5]], [4, 2, 8], 8, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285011,"parameters":{"matrix":[[-2,0,3],[-2,2,5]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-2,0,3],[-2,2,5]]}"}},"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-r05-bounded-linear-operator-0012","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[-1,1,-5],[-1,1,-3]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 1, -5], [-1, 1, -3]], [2, 2, 8], 8, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[-1, 1, -5], [-1, 1, -3]], [2, 2, 8], 8, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285012,"parameters":{"matrix":[[-1,1,-5],[-1,1,-3]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[-1,1,-5],[-1,1,-3]]}"}},"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-r05-bounded-linear-operator-0013","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[0,2,-2],[0,0,2]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 2, -2], [0, 0, 2]], [0, 2, 4], 4, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[0, 2, -2], [0, 0, 2]], [0, 2, 4], 4, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285013,"parameters":{"matrix":[[0,2,-2],[0,0,2]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[0,2,-2],[0,0,2]]}"}},"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-r05-bounded-linear-operator-0014","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[1,3,1],[1,-1,-6]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[1, 3, 1], [1, -1, -6]], [2, 4, 7], 7, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[1, 3, 1], [1, -1, -6]], [2, 4, 7], 7, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285014,"parameters":{"matrix":[[1,3,1],[1,-1,-6]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[1,3,1],[1,-1,-6]]}"}},"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-r05-bounded-linear-operator-0015","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[2,-3,4],[2,-2,-1]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[2, -3, 4], [2, -2, -1]], [4, 5, 5], 5, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[2, -3, 4], [2, -2, -1]], [4, 5, 5], 5, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285015,"parameters":{"matrix":[[2,-3,4],[2,-2,-1]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[2,-3,4],[2,-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-r05-bounded-linear-operator-0016","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[3,-2,-4],[-2,-3,4]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[3, -2, -4], [-2, -3, 4]], [5, 5, 8], 8, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[3, -2, -4], [-2, -3, 4]], [5, 5, 8], 8, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285016,"parameters":{"matrix":[[3,-2,-4],[-2,-3,4]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[3,-2,-4],[-2,-3,4]]}"}},"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-r05-bounded-linear-operator-0017","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[4,-1,-1],[-1,-4,-4]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[4, -1, -1], [-1, -4, -4]], [5, 5, 5], 5, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[4, -1, -1], [-1, -4, -4]], [5, 5, 5], 5, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285017,"parameters":{"matrix":[[4,-1,-1],[-1,-4,-4]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[4,-1,-1],[-1,-4,-4]]}"}},"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-r05-bounded-linear-operator-0018","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[5,0,2],[0,-5,1]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[5, 0, 2], [0, -5, 1]], [5, 5, 3], 5, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[5, 0, 2], [0, -5, 1]], [5, 5, 3], 5, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285018,"parameters":{"matrix":[[5,0,2],[0,-5,1]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[5,0,2],[0,-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-r05-bounded-linear-operator-0019","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[6,1,5],[1,-6,6]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[6, 1, 5], [1, -6, 6]], [7, 7, 11], 11, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[6, 1, 5], [1, -6, 6]], [7, 7, 11], 11, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285019,"parameters":{"matrix":[[6,1,5],[1,-6,6]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[6,1,5],[1,-6,6]]}"}},"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-r05-bounded-linear-operator-0020","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[7,2,-3],[2,-7,-2]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[7, 2, -3], [2, -7, -2]], [9, 9, 5], 9, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[7, 2, -3], [2, -7, -2]], [9, 9, 5], 9, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285020,"parameters":{"matrix":[[7,2,-3],[2,-7,-2]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[7,2,-3],[2,-7,-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-r05-bounded-linear-operator-0021","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[8,3,0],[-2,-8,3]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[8, 3, 0], [-2, -8, 3]], [10, 11, 3], 11, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[8, 3, 0], [-2, -8, 3]], [10, 11, 3], 11, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285021,"parameters":{"matrix":[[8,3,0],[-2,-8,3]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[8,3,0],[-2,-8,3]]}"}},"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-r05-bounded-linear-operator-0022","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[9,-3,3],[-1,-9,-5]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[9, -3, 3], [-1, -9, -5]], [10, 12, 8], 12, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[9, -3, 3], [-1, -9, -5]], [10, 12, 8], 12, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285022,"parameters":{"matrix":[[9,-3,3],[-1,-9,-5]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[9,-3,3],[-1,-9,-5]]}"}},"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-r05-bounded-linear-operator-0023","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[10,-2,-5],[0,-10,0]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[10, -2, -5], [0, -10, 0]], [10, 12, 5], 12, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[10, -2, -5], [0, -10, 0]], [10, 12, 5], 12, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285023,"parameters":{"matrix":[[10,-2,-5],[0,-10,0]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[10,-2,-5],[0,-10,0]]}"}},"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-r05-bounded-linear-operator-0024","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[11,-1,-2],[1,-11,5]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[11, -1, -2], [1, -11, 5]], [12, 12, 7], 12, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[11, -1, -2], [1, -11, 5]], [12, 12, 7], 12, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285024,"parameters":{"matrix":[[11,-1,-2],[1,-11,5]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[11,-1,-2],[1,-11,5]]}"}},"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-r05-bounded-linear-operator-0025","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-l1-norm；資料={\"matrix\":[[12,0,1],[2,-12,-3]]}。請依 [matrix,column_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[12, 0, 1], [2, -12, -3]], [14, 12, 4], 14, maximum_absolute_column_sum)","explanation_zh":"Wave4第二層核對=([[12, 0, 1], [2, -12, -3]], [14, 12, 4], 14, maximum_absolute_column_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-l1-norm","seed":202610285025,"parameters":{"matrix":[[12,0,1],[2,-12,-3]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-l1-norm","semantic_template":"qf-mod28-operator-l1-norm/{\"matrix\":[[12,0,1],[2,-12,-3]]}"}},"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-r05-bounded-linear-operator-0026","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-12,-3,-5],[-2,12,-6]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-12, -3, -5], [-2, 12, -6]], [20, 20], 20, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-12, -3, -5], [-2, 12, -6]], [20, 20], 20, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285026,"parameters":{"matrix":[[-12,-3,-5],[-2,12,-6]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-12,-3,-5],[-2,12,-6]]}"}},"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-r05-bounded-linear-operator-0027","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-11,-2,-2],[-1,11,-1]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-11, -2, -2], [-1, 11, -1]], [15, 13], 15, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-11, -2, -2], [-1, 11, -1]], [15, 13], 15, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285027,"parameters":{"matrix":[[-11,-2,-2],[-1,11,-1]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-11,-2,-2],[-1,11,-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-r05-bounded-linear-operator-0028","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-10,-1,1],[0,10,4]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-10, -1, 1], [0, 10, 4]], [12, 14], 14, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-10, -1, 1], [0, 10, 4]], [12, 14], 14, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285028,"parameters":{"matrix":[[-10,-1,1],[0,10,4]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-10,-1,1],[0,10,4]]}"}},"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-r05-bounded-linear-operator-0029","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-9,0,4],[1,9,-4]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-9, 0, 4], [1, 9, -4]], [13, 14], 14, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-9, 0, 4], [1, 9, -4]], [13, 14], 14, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285029,"parameters":{"matrix":[[-9,0,4],[1,9,-4]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-9,0,4],[1,9,-4]]}"}},"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-r05-bounded-linear-operator-0030","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-8,1,-4],[2,8,1]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-8, 1, -4], [2, 8, 1]], [13, 11], 13, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-8, 1, -4], [2, 8, 1]], [13, 11], 13, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285030,"parameters":{"matrix":[[-8,1,-4],[2,8,1]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-8,1,-4],[2,8,1]]}"}},"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-r05-bounded-linear-operator-0031","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-7,2,-1],[-2,7,6]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-7, 2, -1], [-2, 7, 6]], [10, 15], 15, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-7, 2, -1], [-2, 7, 6]], [10, 15], 15, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285031,"parameters":{"matrix":[[-7,2,-1],[-2,7,6]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-7,2,-1],[-2,7,6]]}"}},"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-r05-bounded-linear-operator-0032","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-6,3,2],[-1,6,-2]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-6, 3, 2], [-1, 6, -2]], [11, 9], 11, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-6, 3, 2], [-1, 6, -2]], [11, 9], 11, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285032,"parameters":{"matrix":[[-6,3,2],[-1,6,-2]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-6,3,2],[-1,6,-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-r05-bounded-linear-operator-0033","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-5,-3,5],[0,5,3]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-5, -3, 5], [0, 5, 3]], [13, 8], 13, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-5, -3, 5], [0, 5, 3]], [13, 8], 13, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285033,"parameters":{"matrix":[[-5,-3,5],[0,5,3]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-5,-3,5],[0,5,3]]}"}},"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-r05-bounded-linear-operator-0034","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-4,-2,-3],[1,4,-5]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-4, -2, -3], [1, 4, -5]], [9, 10], 10, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-4, -2, -3], [1, 4, -5]], [9, 10], 10, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285034,"parameters":{"matrix":[[-4,-2,-3],[1,4,-5]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-4,-2,-3],[1,4,-5]]}"}},"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-r05-bounded-linear-operator-0035","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-3,-1,0],[2,3,0]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-3, -1, 0], [2, 3, 0]], [4, 5], 5, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-3, -1, 0], [2, 3, 0]], [4, 5], 5, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285035,"parameters":{"matrix":[[-3,-1,0],[2,3,0]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-3,-1,0],[2,3,0]]}"}},"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-r05-bounded-linear-operator-0036","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-2,0,3],[-2,2,5]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-2, 0, 3], [-2, 2, 5]], [5, 9], 9, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-2, 0, 3], [-2, 2, 5]], [5, 9], 9, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285036,"parameters":{"matrix":[[-2,0,3],[-2,2,5]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-2,0,3],[-2,2,5]]}"}},"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-r05-bounded-linear-operator-0037","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[-1,1,-5],[-1,1,-3]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 1, -5], [-1, 1, -3]], [7, 5], 7, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[-1, 1, -5], [-1, 1, -3]], [7, 5], 7, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285037,"parameters":{"matrix":[[-1,1,-5],[-1,1,-3]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[-1,1,-5],[-1,1,-3]]}"}},"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-r05-bounded-linear-operator-0038","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[0,2,-2],[0,0,2]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[0, 2, -2], [0, 0, 2]], [4, 2], 4, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[0, 2, -2], [0, 0, 2]], [4, 2], 4, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285038,"parameters":{"matrix":[[0,2,-2],[0,0,2]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[0,2,-2],[0,0,2]]}"}},"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-r05-bounded-linear-operator-0039","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[1,3,1],[1,-1,-6]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[1, 3, 1], [1, -1, -6]], [5, 8], 8, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[1, 3, 1], [1, -1, -6]], [5, 8], 8, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285039,"parameters":{"matrix":[[1,3,1],[1,-1,-6]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[1,3,1],[1,-1,-6]]}"}},"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-r05-bounded-linear-operator-0040","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[2,-3,4],[2,-2,-1]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[2, -3, 4], [2, -2, -1]], [9, 5], 9, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[2, -3, 4], [2, -2, -1]], [9, 5], 9, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285040,"parameters":{"matrix":[[2,-3,4],[2,-2,-1]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[2,-3,4],[2,-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-r05-bounded-linear-operator-0041","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[3,-2,-4],[-2,-3,4]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[3, -2, -4], [-2, -3, 4]], [9, 9], 9, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[3, -2, -4], [-2, -3, 4]], [9, 9], 9, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285041,"parameters":{"matrix":[[3,-2,-4],[-2,-3,4]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[3,-2,-4],[-2,-3,4]]}"}},"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-r05-bounded-linear-operator-0042","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[4,-1,-1],[-1,-4,-4]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[4, -1, -1], [-1, -4, -4]], [6, 9], 9, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[4, -1, -1], [-1, -4, -4]], [6, 9], 9, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285042,"parameters":{"matrix":[[4,-1,-1],[-1,-4,-4]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[4,-1,-1],[-1,-4,-4]]}"}},"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-r05-bounded-linear-operator-0043","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[5,0,2],[0,-5,1]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[5, 0, 2], [0, -5, 1]], [7, 6], 7, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[5, 0, 2], [0, -5, 1]], [7, 6], 7, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285043,"parameters":{"matrix":[[5,0,2],[0,-5,1]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[5,0,2],[0,-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-r05-bounded-linear-operator-0044","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[6,1,5],[1,-6,6]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[6, 1, 5], [1, -6, 6]], [12, 13], 13, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[6, 1, 5], [1, -6, 6]], [12, 13], 13, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285044,"parameters":{"matrix":[[6,1,5],[1,-6,6]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[6,1,5],[1,-6,6]]}"}},"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-r05-bounded-linear-operator-0045","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[7,2,-3],[2,-7,-2]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[7, 2, -3], [2, -7, -2]], [12, 11], 12, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[7, 2, -3], [2, -7, -2]], [12, 11], 12, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285045,"parameters":{"matrix":[[7,2,-3],[2,-7,-2]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[7,2,-3],[2,-7,-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-r05-bounded-linear-operator-0046","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[8,3,0],[-2,-8,3]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[8, 3, 0], [-2, -8, 3]], [11, 13], 13, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[8, 3, 0], [-2, -8, 3]], [11, 13], 13, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285046,"parameters":{"matrix":[[8,3,0],[-2,-8,3]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[8,3,0],[-2,-8,3]]}"}},"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-r05-bounded-linear-operator-0047","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[9,-3,3],[-1,-9,-5]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[9, -3, 3], [-1, -9, -5]], [15, 15], 15, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[9, -3, 3], [-1, -9, -5]], [15, 15], 15, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285047,"parameters":{"matrix":[[9,-3,3],[-1,-9,-5]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[9,-3,3],[-1,-9,-5]]}"}},"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-r05-bounded-linear-operator-0048","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[10,-2,-5],[0,-10,0]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[10, -2, -5], [0, -10, 0]], [17, 10], 17, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[10, -2, -5], [0, -10, 0]], [17, 10], 17, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285048,"parameters":{"matrix":[[10,-2,-5],[0,-10,0]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[10,-2,-5],[0,-10,0]]}"}},"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-r05-bounded-linear-operator-0049","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[11,-1,-2],[1,-11,5]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[11, -1, -2], [1, -11, 5]], [14, 17], 17, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[11, -1, -2], [1, -11, 5]], [14, 17], 17, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285049,"parameters":{"matrix":[[11,-1,-2],[1,-11,5]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[11,-1,-2],[1,-11,5]]}"}},"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-r05-bounded-linear-operator-0050","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-linfinity-norm；資料={\"matrix\":[[12,0,1],[2,-12,-3]]}。請依 [matrix,row_sums,operator_norm,certificate] 欄序回答。","answer":{"kind":"expression","value":"([[12, 0, 1], [2, -12, -3]], [13, 17], 17, maximum_absolute_row_sum)","explanation_zh":"Wave4第二層核對=([[12, 0, 1], [2, -12, -3]], [13, 17], 17, maximum_absolute_row_sum)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-linfinity-norm","seed":202610285050,"parameters":{"matrix":[[12,0,1],[2,-12,-3]],"domain":"Exact_matrix_induced_operator_norm","operation":"operator-linfinity-norm","semantic_template":"qf-mod28-operator-linfinity-norm/{\"matrix\":[[12,0,1],[2,-12,-3]]}"}},"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-r05-bounded-linear-operator-0051","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-12,-3,-5],[-2,12,-6]],\"norm_name\":\"l1\",\"vector\":[-4,-2,-3],\"C\":14}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-4, -2, -3], [69, 2], 9, 71, 14, 126, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [-4, -2, -3], [69, 2], 9, 71, 14, 126, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285051,"parameters":{"matrix":[[-12,-3,-5],[-2,12,-6]],"norm_name":"l1","vector":[-4,-2,-3],"C":14,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":14,\"matrix\":[[-12,-3,-5],[-2,12,-6]],\"norm_name\":\"l1\",\"vector\":[-4,-2,-3]}"}},"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-r05-bounded-linear-operator-0052","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-11,-2,-2],[-1,11,-1]],\"norm_name\":\"linfinity\",\"vector\":[-3,-1,-2],\"C\":16}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-3, -1, -2], [39, -6], 3, 39, 16, 48, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [-3, -1, -2], [39, -6], 3, 39, 16, 48, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285052,"parameters":{"matrix":[[-11,-2,-2],[-1,11,-1]],"norm_name":"linfinity","vector":[-3,-1,-2],"C":16,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":16,\"matrix\":[[-11,-2,-2],[-1,11,-1]],\"norm_name\":\"linfinity\",\"vector\":[-3,-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-r05-bounded-linear-operator-0053","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-10,-1,1],[0,10,4]],\"norm_name\":\"l1\",\"vector\":[-2,0,-1],\"C\":13}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-2, 0, -1], [19, -4], 3, 23, 13, 39, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [-2, 0, -1], [19, -4], 3, 23, 13, 39, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285053,"parameters":{"matrix":[[-10,-1,1],[0,10,4]],"norm_name":"l1","vector":[-2,0,-1],"C":13,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":13,\"matrix\":[[-10,-1,1],[0,10,4]],\"norm_name\":\"l1\",\"vector\":[-2,0,-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-r05-bounded-linear-operator-0054","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-9,0,4],[1,9,-4]],\"norm_name\":\"linfinity\",\"vector\":[-1,1,0],\"C\":14}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-1, 1, 0], [9, 8], 1, 9, 14, 14, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [-1, 1, 0], [9, 8], 1, 9, 14, 14, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285054,"parameters":{"matrix":[[-9,0,4],[1,9,-4]],"norm_name":"linfinity","vector":[-1,1,0],"C":14,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":14,\"matrix\":[[-9,0,4],[1,9,-4]],\"norm_name\":\"linfinity\",\"vector\":[-1,1,0]}"}},"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-r05-bounded-linear-operator-0055","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-8,1,-4],[2,8,1]],\"norm_name\":\"l1\",\"vector\":[0,2,1],\"C\":9}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [0, 2, 1], [-2, 17], 3, 19, 9, 27, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [0, 2, 1], [-2, 17], 3, 19, 9, 27, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285055,"parameters":{"matrix":[[-8,1,-4],[2,8,1]],"norm_name":"l1","vector":[0,2,1],"C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":9,\"matrix\":[[-8,1,-4],[2,8,1]],\"norm_name\":\"l1\",\"vector\":[0,2,1]}"}},"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-r05-bounded-linear-operator-0056","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-7,2,-1],[-2,7,6]],\"norm_name\":\"linfinity\",\"vector\":[1,-2,2],\"C\":17}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [1, -2, 2], [-13, -4], 2, 13, 17, 34, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [1, -2, 2], [-13, -4], 2, 13, 17, 34, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285056,"parameters":{"matrix":[[-7,2,-1],[-2,7,6]],"norm_name":"linfinity","vector":[1,-2,2],"C":17,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":17,\"matrix\":[[-7,2,-1],[-2,7,6]],\"norm_name\":\"linfinity\",\"vector\":[1,-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-r05-bounded-linear-operator-0057","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-6,3,2],[-1,6,-2]],\"norm_name\":\"l1\",\"vector\":[2,-1,3],\"C\":9}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [2, -1, 3], [-9, -14], 6, 23, 9, 54, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [2, -1, 3], [-9, -14], 6, 23, 9, 54, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285057,"parameters":{"matrix":[[-6,3,2],[-1,6,-2]],"norm_name":"l1","vector":[2,-1,3],"C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":9,\"matrix\":[[-6,3,2],[-1,6,-2]],\"norm_name\":\"l1\",\"vector\":[2,-1,3]}"}},"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-r05-bounded-linear-operator-0058","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-5,-3,5],[0,5,3]],\"norm_name\":\"linfinity\",\"vector\":[3,0,-3],\"C\":14}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [3, 0, -3], [-30, -9], 3, 30, 14, 42, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [3, 0, -3], [-30, -9], 3, 30, 14, 42, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285058,"parameters":{"matrix":[[-5,-3,5],[0,5,3]],"norm_name":"linfinity","vector":[3,0,-3],"C":14,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":14,\"matrix\":[[-5,-3,5],[0,5,3]],\"norm_name\":\"linfinity\",\"vector\":[3,0,-3]}"}},"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-r05-bounded-linear-operator-0059","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-4,-2,-3],[1,4,-5]],\"norm_name\":\"l1\",\"vector\":[4,1,-2],\"C\":7}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [4, 1, -2], [-12, 18], 7, 30, 7, 49, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [4, 1, -2], [-12, 18], 7, 30, 7, 49, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285059,"parameters":{"matrix":[[-4,-2,-3],[1,4,-5]],"norm_name":"l1","vector":[4,1,-2],"C":7,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":7,\"matrix\":[[-4,-2,-3],[1,4,-5]],\"norm_name\":\"l1\",\"vector\":[4,1,-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-r05-bounded-linear-operator-0060","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-3,-1,0],[2,3,0]],\"norm_name\":\"linfinity\",\"vector\":[-4,2,-1],\"C\":5}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-4, 2, -1], [10, -2], 4, 10, 5, 20, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [-4, 2, -1], [10, -2], 4, 10, 5, 20, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285060,"parameters":{"matrix":[[-3,-1,0],[2,3,0]],"norm_name":"linfinity","vector":[-4,2,-1],"C":5,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":5,\"matrix\":[[-3,-1,0],[2,3,0]],\"norm_name\":\"linfinity\",\"vector\":[-4,2,-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-r05-bounded-linear-operator-0061","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-2,0,3],[-2,2,5]],\"norm_name\":\"l1\",\"vector\":[-3,-2,0],\"C\":9}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-3, -2, 0], [6, 2], 5, 8, 9, 45, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [-3, -2, 0], [6, 2], 5, 8, 9, 45, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285061,"parameters":{"matrix":[[-2,0,3],[-2,2,5]],"norm_name":"l1","vector":[-3,-2,0],"C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":9,\"matrix\":[[-2,0,3],[-2,2,5]],\"norm_name\":\"l1\",\"vector\":[-3,-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-r05-bounded-linear-operator-0062","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[-1,1,-5],[-1,1,-3]],\"norm_name\":\"linfinity\",\"vector\":[-2,-1,1],\"C\":9}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-2, -1, 1], [-4, -2], 2, 4, 9, 18, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [-2, -1, 1], [-4, -2], 2, 4, 9, 18, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285062,"parameters":{"matrix":[[-1,1,-5],[-1,1,-3]],"norm_name":"linfinity","vector":[-2,-1,1],"C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":9,\"matrix\":[[-1,1,-5],[-1,1,-3]],\"norm_name\":\"linfinity\",\"vector\":[-2,-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-r05-bounded-linear-operator-0063","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[0,2,-2],[0,0,2]],\"norm_name\":\"l1\",\"vector\":[-1,0,2],\"C\":3}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-1, 0, 2], [-4, 4], 3, 8, 3, 9, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [-1, 0, 2], [-4, 4], 3, 8, 3, 9, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285063,"parameters":{"matrix":[[0,2,-2],[0,0,2]],"norm_name":"l1","vector":[-1,0,2],"C":3,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":3,\"matrix\":[[0,2,-2],[0,0,2]],\"norm_name\":\"l1\",\"vector\":[-1,0,2]}"}},"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-r05-bounded-linear-operator-0064","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[1,3,1],[1,-1,-6]],\"norm_name\":\"linfinity\",\"vector\":[0,1,3],\"C\":9}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [0, 1, 3], [6, -19], 3, 19, 9, 27, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [0, 1, 3], [6, -19], 3, 19, 9, 27, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285064,"parameters":{"matrix":[[1,3,1],[1,-1,-6]],"norm_name":"linfinity","vector":[0,1,3],"C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":9,\"matrix\":[[1,3,1],[1,-1,-6]],\"norm_name\":\"linfinity\",\"vector\":[0,1,3]}"}},"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-r05-bounded-linear-operator-0065","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[2,-3,4],[2,-2,-1]],\"norm_name\":\"l1\",\"vector\":[1,2,-3],\"C\":7}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [1, 2, -3], [-16, 1], 6, 17, 7, 42, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [1, 2, -3], [-16, 1], 6, 17, 7, 42, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285065,"parameters":{"matrix":[[2,-3,4],[2,-2,-1]],"norm_name":"l1","vector":[1,2,-3],"C":7,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":7,\"matrix\":[[2,-3,4],[2,-2,-1]],\"norm_name\":\"l1\",\"vector\":[1,2,-3]}"}},"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-r05-bounded-linear-operator-0066","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[3,-2,-4],[-2,-3,4]],\"norm_name\":\"linfinity\",\"vector\":[2,-2,-2],\"C\":9}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [2, -2, -2], [18, -6], 2, 18, 9, 18, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [2, -2, -2], [18, -6], 2, 18, 9, 18, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285066,"parameters":{"matrix":[[3,-2,-4],[-2,-3,4]],"norm_name":"linfinity","vector":[2,-2,-2],"C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":9,\"matrix\":[[3,-2,-4],[-2,-3,4]],\"norm_name\":\"linfinity\",\"vector\":[2,-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-r05-bounded-linear-operator-0067","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[4,-1,-1],[-1,-4,-4]],\"norm_name\":\"l1\",\"vector\":[3,-1,-1],\"C\":4}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [3, -1, -1], [14, 5], 5, 19, 4, 20, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [3, -1, -1], [14, 5], 5, 19, 4, 20, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285067,"parameters":{"matrix":[[4,-1,-1],[-1,-4,-4]],"norm_name":"l1","vector":[3,-1,-1],"C":4,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":4,\"matrix\":[[4,-1,-1],[-1,-4,-4]],\"norm_name\":\"l1\",\"vector\":[3,-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-r05-bounded-linear-operator-0068","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[5,0,2],[0,-5,1]],\"norm_name\":\"linfinity\",\"vector\":[4,0,0],\"C\":9}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [4, 0, 0], [20, 0], 4, 20, 9, 36, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [4, 0, 0], [20, 0], 4, 20, 9, 36, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285068,"parameters":{"matrix":[[5,0,2],[0,-5,1]],"norm_name":"linfinity","vector":[4,0,0],"C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":9,\"matrix\":[[5,0,2],[0,-5,1]],\"norm_name\":\"linfinity\",\"vector\":[4,0,0]}"}},"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-r05-bounded-linear-operator-0069","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[6,1,5],[1,-6,6]],\"norm_name\":\"l1\",\"vector\":[-4,1,1],\"C\":11}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-4, 1, 1], [-18, -4], 6, 22, 11, 66, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [-4, 1, 1], [-18, -4], 6, 22, 11, 66, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285069,"parameters":{"matrix":[[6,1,5],[1,-6,6]],"norm_name":"l1","vector":[-4,1,1],"C":11,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":11,\"matrix\":[[6,1,5],[1,-6,6]],\"norm_name\":\"l1\",\"vector\":[-4,1,1]}"}},"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-r05-bounded-linear-operator-0070","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[7,2,-3],[2,-7,-2]],\"norm_name\":\"linfinity\",\"vector\":[-3,2,2],\"C\":13}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-3, 2, 2], [-23, -24], 3, 24, 13, 39, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [-3, 2, 2], [-23, -24], 3, 24, 13, 39, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285070,"parameters":{"matrix":[[7,2,-3],[2,-7,-2]],"norm_name":"linfinity","vector":[-3,2,2],"C":13,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":13,\"matrix\":[[7,2,-3],[2,-7,-2]],\"norm_name\":\"linfinity\",\"vector\":[-3,2,2]}"}},"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-r05-bounded-linear-operator-0071","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[8,3,0],[-2,-8,3]],\"norm_name\":\"l1\",\"vector\":[-2,-2,3],\"C\":10}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-2, -2, 3], [-22, 29], 7, 51, 10, 70, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [-2, -2, 3], [-22, 29], 7, 51, 10, 70, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285071,"parameters":{"matrix":[[8,3,0],[-2,-8,3]],"norm_name":"l1","vector":[-2,-2,3],"C":10,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":10,\"matrix\":[[8,3,0],[-2,-8,3]],\"norm_name\":\"l1\",\"vector\":[-2,-2,3]}"}},"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-r05-bounded-linear-operator-0072","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[9,-3,3],[-1,-9,-5]],\"norm_name\":\"linfinity\",\"vector\":[-1,-1,-3],\"C\":15}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-1, -1, -3], [-15, 25], 3, 25, 15, 45, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [-1, -1, -3], [-15, 25], 3, 25, 15, 45, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285072,"parameters":{"matrix":[[9,-3,3],[-1,-9,-5]],"norm_name":"linfinity","vector":[-1,-1,-3],"C":15,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":15,\"matrix\":[[9,-3,3],[-1,-9,-5]],\"norm_name\":\"linfinity\",\"vector\":[-1,-1,-3]}"}},"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-r05-bounded-linear-operator-0073","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[10,-2,-5],[0,-10,0]],\"norm_name\":\"l1\",\"vector\":[0,0,-2],\"C\":13}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [0, 0, -2], [10, 0], 2, 10, 13, 26, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [0, 0, -2], [10, 0], 2, 10, 13, 26, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285073,"parameters":{"matrix":[[10,-2,-5],[0,-10,0]],"norm_name":"l1","vector":[0,0,-2],"C":13,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":13,\"matrix\":[[10,-2,-5],[0,-10,0]],\"norm_name\":\"l1\",\"vector\":[0,0,-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-r05-bounded-linear-operator-0074","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[11,-1,-2],[1,-11,5]],\"norm_name\":\"linfinity\",\"vector\":[1,1,-1],\"C\":19}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [1, 1, -1], [12, -15], 1, 15, 19, 19, 是, instance_only)","explanation_zh":"Wave4第二層核對=(linfinity, [1, 1, -1], [12, -15], 1, 15, 19, 19, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285074,"parameters":{"matrix":[[11,-1,-2],[1,-11,5]],"norm_name":"linfinity","vector":[1,1,-1],"C":19,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":19,\"matrix\":[[11,-1,-2],[1,-11,5]],\"norm_name\":\"linfinity\",\"vector\":[1,1,-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-r05-bounded-linear-operator-0075","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bound-instance；資料={\"matrix\":[[12,0,1],[2,-12,-3]],\"norm_name\":\"l1\",\"vector\":[2,2,0],\"C\":13}。請依 [norm_name,vector,image,input_norm,output_norm,C,rhs,pass,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, [2, 2, 0], [24, -20], 4, 44, 13, 52, 是, instance_only)","explanation_zh":"Wave4第二層核對=(l1, [2, 2, 0], [24, -20], 4, 44, 13, 52, 是, instance_only)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bound-instance","seed":202610285075,"parameters":{"matrix":[[12,0,1],[2,-12,-3]],"norm_name":"l1","vector":[2,2,0],"C":13,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bound-instance","semantic_template":"qf-mod28-operator-bound-instance/{\"C\":13,\"matrix\":[[12,0,1],[2,-12,-3]],\"norm_name\":\"l1\",\"vector\":[2,2,0]}"}},"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-r05-bounded-linear-operator-0076","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-12,-3,-5],[-2,12,-6]],\"norm_name\":\"l1\",\"C\":14}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 15, 14, 否, 否, bound_too_small)","explanation_zh":"Wave4第二層核對=(l1, 15, 14, 否, 否, bound_too_small)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285076,"parameters":{"matrix":[[-12,-3,-5],[-2,12,-6]],"norm_name":"l1","C":14,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":14,\"matrix\":[[-12,-3,-5],[-2,12,-6]],\"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-r05-bounded-linear-operator-0077","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-11,-2,-2],[-1,11,-1]],\"norm_name\":\"linfinity\",\"C\":16}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 15, 16, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 15, 16, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285077,"parameters":{"matrix":[[-11,-2,-2],[-1,11,-1]],"norm_name":"linfinity","C":16,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":16,\"matrix\":[[-11,-2,-2],[-1,11,-1]],\"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-r05-bounded-linear-operator-0078","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-10,-1,1],[0,10,4]],\"norm_name\":\"l1\",\"C\":13}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 11, 13, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(l1, 11, 13, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285078,"parameters":{"matrix":[[-10,-1,1],[0,10,4]],"norm_name":"l1","C":13,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":13,\"matrix\":[[-10,-1,1],[0,10,4]],\"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-r05-bounded-linear-operator-0079","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-9,0,4],[1,9,-4]],\"norm_name\":\"linfinity\",\"C\":14}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 14, 14, 是, 是, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 14, 14, 是, 是, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285079,"parameters":{"matrix":[[-9,0,4],[1,9,-4]],"norm_name":"linfinity","C":14,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":14,\"matrix\":[[-9,0,4],[1,9,-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-r05-bounded-linear-operator-0080","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-8,1,-4],[2,8,1]],\"norm_name\":\"l1\",\"C\":9}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 10, 9, 否, 否, bound_too_small)","explanation_zh":"Wave4第二層核對=(l1, 10, 9, 否, 否, bound_too_small)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285080,"parameters":{"matrix":[[-8,1,-4],[2,8,1]],"norm_name":"l1","C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":9,\"matrix\":[[-8,1,-4],[2,8,1]],\"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-r05-bounded-linear-operator-0081","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-7,2,-1],[-2,7,6]],\"norm_name\":\"linfinity\",\"C\":17}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 15, 17, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 15, 17, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285081,"parameters":{"matrix":[[-7,2,-1],[-2,7,6]],"norm_name":"linfinity","C":17,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":17,\"matrix\":[[-7,2,-1],[-2,7,6]],\"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-r05-bounded-linear-operator-0082","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-6,3,2],[-1,6,-2]],\"norm_name\":\"l1\",\"C\":9}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 9, 9, 是, 是, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(l1, 9, 9, 是, 是, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285082,"parameters":{"matrix":[[-6,3,2],[-1,6,-2]],"norm_name":"l1","C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":9,\"matrix\":[[-6,3,2],[-1,6,-2]],\"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-r05-bounded-linear-operator-0083","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-5,-3,5],[0,5,3]],\"norm_name\":\"linfinity\",\"C\":14}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 13, 14, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 13, 14, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285083,"parameters":{"matrix":[[-5,-3,5],[0,5,3]],"norm_name":"linfinity","C":14,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":14,\"matrix\":[[-5,-3,5],[0,5,3]],\"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-r05-bounded-linear-operator-0084","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-4,-2,-3],[1,4,-5]],\"norm_name\":\"l1\",\"C\":7}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 8, 7, 否, 否, bound_too_small)","explanation_zh":"Wave4第二層核對=(l1, 8, 7, 否, 否, bound_too_small)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285084,"parameters":{"matrix":[[-4,-2,-3],[1,4,-5]],"norm_name":"l1","C":7,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":7,\"matrix\":[[-4,-2,-3],[1,4,-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-r05-bounded-linear-operator-0085","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-3,-1,0],[2,3,0]],\"norm_name\":\"linfinity\",\"C\":5}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 5, 5, 是, 是, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 5, 5, 是, 是, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285085,"parameters":{"matrix":[[-3,-1,0],[2,3,0]],"norm_name":"linfinity","C":5,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":5,\"matrix\":[[-3,-1,0],[2,3,0]],\"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-r05-bounded-linear-operator-0086","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-2,0,3],[-2,2,5]],\"norm_name\":\"l1\",\"C\":9}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 8, 9, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(l1, 8, 9, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285086,"parameters":{"matrix":[[-2,0,3],[-2,2,5]],"norm_name":"l1","C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":9,\"matrix\":[[-2,0,3],[-2,2,5]],\"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-r05-bounded-linear-operator-0087","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[-1,1,-5],[-1,1,-3]],\"norm_name\":\"linfinity\",\"C\":9}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 7, 9, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 7, 9, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285087,"parameters":{"matrix":[[-1,1,-5],[-1,1,-3]],"norm_name":"linfinity","C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":9,\"matrix\":[[-1,1,-5],[-1,1,-3]],\"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-r05-bounded-linear-operator-0088","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[0,2,-2],[0,0,2]],\"norm_name\":\"l1\",\"C\":3}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 4, 3, 否, 否, bound_too_small)","explanation_zh":"Wave4第二層核對=(l1, 4, 3, 否, 否, bound_too_small)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285088,"parameters":{"matrix":[[0,2,-2],[0,0,2]],"norm_name":"l1","C":3,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":3,\"matrix\":[[0,2,-2],[0,0,2]],\"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-r05-bounded-linear-operator-0089","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[1,3,1],[1,-1,-6]],\"norm_name\":\"linfinity\",\"C\":9}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 8, 9, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 8, 9, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285089,"parameters":{"matrix":[[1,3,1],[1,-1,-6]],"norm_name":"linfinity","C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":9,\"matrix\":[[1,3,1],[1,-1,-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-r05-bounded-linear-operator-0090","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[2,-3,4],[2,-2,-1]],\"norm_name\":\"l1\",\"C\":7}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 5, 7, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(l1, 5, 7, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285090,"parameters":{"matrix":[[2,-3,4],[2,-2,-1]],"norm_name":"l1","C":7,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":7,\"matrix\":[[2,-3,4],[2,-2,-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-r05-bounded-linear-operator-0091","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[3,-2,-4],[-2,-3,4]],\"norm_name\":\"linfinity\",\"C\":9}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 9, 9, 是, 是, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 9, 9, 是, 是, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285091,"parameters":{"matrix":[[3,-2,-4],[-2,-3,4]],"norm_name":"linfinity","C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":9,\"matrix\":[[3,-2,-4],[-2,-3,4]],\"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-r05-bounded-linear-operator-0092","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[4,-1,-1],[-1,-4,-4]],\"norm_name\":\"l1\",\"C\":4}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 5, 4, 否, 否, bound_too_small)","explanation_zh":"Wave4第二層核對=(l1, 5, 4, 否, 否, bound_too_small)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285092,"parameters":{"matrix":[[4,-1,-1],[-1,-4,-4]],"norm_name":"l1","C":4,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":4,\"matrix\":[[4,-1,-1],[-1,-4,-4]],\"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-r05-bounded-linear-operator-0093","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[5,0,2],[0,-5,1]],\"norm_name\":\"linfinity\",\"C\":9}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 7, 9, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 7, 9, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285093,"parameters":{"matrix":[[5,0,2],[0,-5,1]],"norm_name":"linfinity","C":9,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":9,\"matrix\":[[5,0,2],[0,-5,1]],\"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-r05-bounded-linear-operator-0094","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[6,1,5],[1,-6,6]],\"norm_name\":\"l1\",\"C\":11}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 11, 11, 是, 是, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(l1, 11, 11, 是, 是, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285094,"parameters":{"matrix":[[6,1,5],[1,-6,6]],"norm_name":"l1","C":11,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":11,\"matrix\":[[6,1,5],[1,-6,6]],\"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-r05-bounded-linear-operator-0095","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[7,2,-3],[2,-7,-2]],\"norm_name\":\"linfinity\",\"C\":13}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 12, 13, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 12, 13, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285095,"parameters":{"matrix":[[7,2,-3],[2,-7,-2]],"norm_name":"linfinity","C":13,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":13,\"matrix\":[[7,2,-3],[2,-7,-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-r05-bounded-linear-operator-0096","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[8,3,0],[-2,-8,3]],\"norm_name\":\"l1\",\"C\":10}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 11, 10, 否, 否, bound_too_small)","explanation_zh":"Wave4第二層核對=(l1, 11, 10, 否, 否, bound_too_small)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285096,"parameters":{"matrix":[[8,3,0],[-2,-8,3]],"norm_name":"l1","C":10,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":10,\"matrix\":[[8,3,0],[-2,-8,3]],\"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-r05-bounded-linear-operator-0097","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[9,-3,3],[-1,-9,-5]],\"norm_name\":\"linfinity\",\"C\":15}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 15, 15, 是, 是, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 15, 15, 是, 是, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285097,"parameters":{"matrix":[[9,-3,3],[-1,-9,-5]],"norm_name":"linfinity","C":15,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":15,\"matrix\":[[9,-3,3],[-1,-9,-5]],\"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-r05-bounded-linear-operator-0098","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[10,-2,-5],[0,-10,0]],\"norm_name\":\"l1\",\"C\":13}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 12, 13, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(l1, 12, 13, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285098,"parameters":{"matrix":[[10,-2,-5],[0,-10,0]],"norm_name":"l1","C":13,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":13,\"matrix\":[[10,-2,-5],[0,-10,0]],\"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-r05-bounded-linear-operator-0099","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[11,-1,-2],[1,-11,5]],\"norm_name\":\"linfinity\",\"C\":19}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 17, 19, 是, 否, uniform_bound_certificate)","explanation_zh":"Wave4第二層核對=(linfinity, 17, 19, 是, 否, uniform_bound_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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285099,"parameters":{"matrix":[[11,-1,-2],[1,-11,5]],"norm_name":"linfinity","C":19,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":19,\"matrix\":[[11,-1,-2],[1,-11,5]],\"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-r05-bounded-linear-operator-0100","batch_id":"batch-20261014-advance-20261028-r05-bounded-linear-operator-foundations","language":"zh-Hant","source_mko_ids":["mko-bounded-linear-operator"],"title_zh":"有界線性算子","stem_zh":"來源與目標norm明示且使用單一統一常數。操作=operator-bounded-certificate；資料={\"matrix\":[[12,0,1],[2,-12,-3]],\"norm_name\":\"l1\",\"C\":13}。請依 [norm_name,exact_operator_norm,C,uniform_bound,optimal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 14, 13, 否, 否, bound_too_small)","explanation_zh":"Wave4第二層核對=(l1, 14, 13, 否, 否, bound_too_small)；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；矩陣誘導operator norm給全稱界證書；instance通過或非最佳上界不冒充exact norm。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有界線性算子"]},"variant":{"family_id":"qf-mod28-operator-bounded-certificate","seed":202610285100,"parameters":{"matrix":[[12,0,1],[2,-12,-3]],"norm_name":"l1","C":13,"domain":"Exact_matrix_induced_operator_norm","operation":"operator-bounded-certificate","semantic_template":"qf-mod28-operator-bounded-certificate/{\"C\":13,\"matrix\":[[12,0,1],[2,-12,-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"}}