{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0001","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-12,-8,-9,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-12, -8, -9, -2], l1, 31)","explanation_zh":"結構深度核對=([-12, -8, -9, -2], l1, 31)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262001,"parameters":{"vector":[-12,-8,-9,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-12,-8,-9,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0002","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-11,-7,-2,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-11, -7, -2, -1], l1, 21)","explanation_zh":"結構深度核對=([-11, -7, -2, -1], l1, 21)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262002,"parameters":{"vector":[-11,-7,-2,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-11,-7,-2,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0003","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-10,-4,5,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-10, -4, 5, 0], l1, 19)","explanation_zh":"結構深度核對=([-10, -4, 5, 0], l1, 19)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262003,"parameters":{"vector":[-10,-4,5,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-10,-4,5,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0004","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-9,1,-7,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-9, 1, -7, 1], l1, 18)","explanation_zh":"結構深度核對=([-9, 1, -7, 1], l1, 18)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262004,"parameters":{"vector":[-9,1,-7,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-9,1,-7,1]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0005","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-8,8,0,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-8, 8, 0, 2], l1, 18)","explanation_zh":"結構深度核對=([-8, 8, 0, 2], l1, 18)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262005,"parameters":{"vector":[-8,8,0,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-8,8,0,2]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0006","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-7,0,7,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-7, 0, 7, -2], l1, 16)","explanation_zh":"結構深度核對=([-7, 0, 7, -2], l1, 16)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262006,"parameters":{"vector":[-7,0,7,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-7,0,7,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0007","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-6,-6,-5,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-6, -6, -5, -1], l1, 18)","explanation_zh":"結構深度核對=([-6, -6, -5, -1], l1, 18)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262007,"parameters":{"vector":[-6,-6,-5,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-6,-6,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0008","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-5,7,2,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-5, 7, 2, 0], l1, 14)","explanation_zh":"結構深度核對=([-5, 7, 2, 0], l1, 14)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262008,"parameters":{"vector":[-5,7,2,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-5,7,2,0]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0009","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-4,5,9,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-4, 5, 9, 1], l1, 19)","explanation_zh":"結構深度核對=([-4, 5, 9, 1], l1, 19)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262009,"parameters":{"vector":[-4,5,9,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-4,5,9,1]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0010","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-3,5,-3,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-3, 5, -3, 2], l1, 13)","explanation_zh":"結構深度核對=([-3, 5, -3, 2], l1, 13)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262010,"parameters":{"vector":[-3,5,-3,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-3,5,-3,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0011","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-2,7,4,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-2, 7, 4, -2], l1, 15)","explanation_zh":"結構深度核對=([-2, 7, 4, -2], l1, 15)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262011,"parameters":{"vector":[-2,7,4,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-2,7,4,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0012","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[-1,-6,-8,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-1, -6, -8, -1], l1, 16)","explanation_zh":"結構深度核對=([-1, -6, -8, -1], l1, 16)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262012,"parameters":{"vector":[-1,-6,-8,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[-1,-6,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0013","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[0,0,-1,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, -1, 0], l1, 1)","explanation_zh":"結構深度核對=([0, 0, -1, 0], l1, 1)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262013,"parameters":{"vector":[0,0,-1,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[0,0,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0014","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[1,8,6,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([1, 8, 6, 1], l1, 16)","explanation_zh":"結構深度核對=([1, 8, 6, 1], l1, 16)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262014,"parameters":{"vector":[1,8,6,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[1,8,6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0015","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[2,1,-6,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, -6, 2], l1, 11)","explanation_zh":"結構深度核對=([2, 1, -6, 2], l1, 11)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262015,"parameters":{"vector":[2,1,-6,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0016","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[3,-4,1,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([3, -4, 1, -2], l1, 10)","explanation_zh":"結構深度核對=([3, -4, 1, -2], l1, 10)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262016,"parameters":{"vector":[3,-4,1,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[3,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0017","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[4,-7,8,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([4, -7, 8, -1], l1, 20)","explanation_zh":"結構深度核對=([4, -7, 8, -1], l1, 20)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262017,"parameters":{"vector":[4,-7,8,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[4,-7,8,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0018","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[5,-8,-4,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([5, -8, -4, 0], l1, 17)","explanation_zh":"結構深度核對=([5, -8, -4, 0], l1, 17)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262018,"parameters":{"vector":[5,-8,-4,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[5,-8,-4,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0019","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[6,-7,3,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([6, -7, 3, 1], l1, 17)","explanation_zh":"結構深度核對=([6, -7, 3, 1], l1, 17)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262019,"parameters":{"vector":[6,-7,3,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[6,-7,3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0020","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[7,-4,-9,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([7, -4, -9, 2], l1, 22)","explanation_zh":"結構深度核對=([7, -4, -9, 2], l1, 22)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262020,"parameters":{"vector":[7,-4,-9,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[7,-4,-9,2]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0021","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[8,1,-2,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([8, 1, -2, -2], l1, 13)","explanation_zh":"結構深度核對=([8, 1, -2, -2], l1, 13)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262021,"parameters":{"vector":[8,1,-2,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[8,1,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0022","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[9,8,5,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([9, 8, 5, -1], l1, 23)","explanation_zh":"結構深度核對=([9, 8, 5, -1], l1, 23)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262022,"parameters":{"vector":[9,8,5,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[9,8,5,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0023","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[10,0,-7,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([10, 0, -7, 0], l1, 17)","explanation_zh":"結構深度核對=([10, 0, -7, 0], l1, 17)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262023,"parameters":{"vector":[10,0,-7,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[10,0,-7,0]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0024","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[11,-6,0,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([11, -6, 0, 1], l1, 18)","explanation_zh":"結構深度核對=([11, -6, 0, 1], l1, 18)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262024,"parameters":{"vector":[11,-6,0,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[11,-6,0,1]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0025","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-l1-evaluate；資料={\"vector\":[12,7,7,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([12, 7, 7, 2], l1, 28)","explanation_zh":"結構深度核對=([12, 7, 7, 2], l1, 28)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-l1-evaluate","seed":202610262025,"parameters":{"vector":[12,7,7,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-l1-evaluate","semantic_template":"qf-mod26-norm-l1-evaluate/{\"vector\":[12,7,7,2]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0026","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-12,-8,-9,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-12, -8, -9, -2], linfinity, 12)","explanation_zh":"結構深度核對=([-12, -8, -9, -2], linfinity, 12)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262026,"parameters":{"vector":[-12,-8,-9,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-12,-8,-9,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0027","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-11,-7,-2,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-11, -7, -2, -1], linfinity, 11)","explanation_zh":"結構深度核對=([-11, -7, -2, -1], linfinity, 11)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262027,"parameters":{"vector":[-11,-7,-2,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-11,-7,-2,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0028","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-10,-4,5,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-10, -4, 5, 0], linfinity, 10)","explanation_zh":"結構深度核對=([-10, -4, 5, 0], linfinity, 10)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262028,"parameters":{"vector":[-10,-4,5,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-10,-4,5,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0029","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-9,1,-7,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-9, 1, -7, 1], linfinity, 9)","explanation_zh":"結構深度核對=([-9, 1, -7, 1], linfinity, 9)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262029,"parameters":{"vector":[-9,1,-7,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-9,1,-7,1]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0030","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-8,8,0,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-8, 8, 0, 2], linfinity, 8)","explanation_zh":"結構深度核對=([-8, 8, 0, 2], linfinity, 8)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262030,"parameters":{"vector":[-8,8,0,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-8,8,0,2]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0031","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-7,0,7,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-7, 0, 7, -2], linfinity, 7)","explanation_zh":"結構深度核對=([-7, 0, 7, -2], linfinity, 7)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262031,"parameters":{"vector":[-7,0,7,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-7,0,7,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0032","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-6,-6,-5,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-6, -6, -5, -1], linfinity, 6)","explanation_zh":"結構深度核對=([-6, -6, -5, -1], linfinity, 6)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262032,"parameters":{"vector":[-6,-6,-5,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-6,-6,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0033","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-5,7,2,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-5, 7, 2, 0], linfinity, 7)","explanation_zh":"結構深度核對=([-5, 7, 2, 0], linfinity, 7)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262033,"parameters":{"vector":[-5,7,2,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-5,7,2,0]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0034","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-4,5,9,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-4, 5, 9, 1], linfinity, 9)","explanation_zh":"結構深度核對=([-4, 5, 9, 1], linfinity, 9)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262034,"parameters":{"vector":[-4,5,9,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-4,5,9,1]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0035","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-3,5,-3,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-3, 5, -3, 2], linfinity, 5)","explanation_zh":"結構深度核對=([-3, 5, -3, 2], linfinity, 5)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262035,"parameters":{"vector":[-3,5,-3,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-3,5,-3,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0036","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-2,7,4,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-2, 7, 4, -2], linfinity, 7)","explanation_zh":"結構深度核對=([-2, 7, 4, -2], linfinity, 7)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262036,"parameters":{"vector":[-2,7,4,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-2,7,4,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0037","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[-1,-6,-8,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([-1, -6, -8, -1], linfinity, 8)","explanation_zh":"結構深度核對=([-1, -6, -8, -1], linfinity, 8)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262037,"parameters":{"vector":[-1,-6,-8,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[-1,-6,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0038","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[0,0,-1,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, -1, 0], linfinity, 1)","explanation_zh":"結構深度核對=([0, 0, -1, 0], linfinity, 1)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262038,"parameters":{"vector":[0,0,-1,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[0,0,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0039","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[1,8,6,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([1, 8, 6, 1], linfinity, 8)","explanation_zh":"結構深度核對=([1, 8, 6, 1], linfinity, 8)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262039,"parameters":{"vector":[1,8,6,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[1,8,6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0040","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[2,1,-6,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, -6, 2], linfinity, 6)","explanation_zh":"結構深度核對=([2, 1, -6, 2], linfinity, 6)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262040,"parameters":{"vector":[2,1,-6,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0041","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[3,-4,1,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([3, -4, 1, -2], linfinity, 4)","explanation_zh":"結構深度核對=([3, -4, 1, -2], linfinity, 4)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262041,"parameters":{"vector":[3,-4,1,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[3,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0042","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[4,-7,8,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([4, -7, 8, -1], linfinity, 8)","explanation_zh":"結構深度核對=([4, -7, 8, -1], linfinity, 8)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262042,"parameters":{"vector":[4,-7,8,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[4,-7,8,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0043","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[5,-8,-4,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([5, -8, -4, 0], linfinity, 8)","explanation_zh":"結構深度核對=([5, -8, -4, 0], linfinity, 8)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262043,"parameters":{"vector":[5,-8,-4,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[5,-8,-4,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0044","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[6,-7,3,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([6, -7, 3, 1], linfinity, 7)","explanation_zh":"結構深度核對=([6, -7, 3, 1], linfinity, 7)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262044,"parameters":{"vector":[6,-7,3,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[6,-7,3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0045","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[7,-4,-9,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([7, -4, -9, 2], linfinity, 9)","explanation_zh":"結構深度核對=([7, -4, -9, 2], linfinity, 9)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262045,"parameters":{"vector":[7,-4,-9,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[7,-4,-9,2]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0046","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[8,1,-2,-2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([8, 1, -2, -2], linfinity, 8)","explanation_zh":"結構深度核對=([8, 1, -2, -2], linfinity, 8)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262046,"parameters":{"vector":[8,1,-2,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[8,1,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0047","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[9,8,5,-1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([9, 8, 5, -1], linfinity, 9)","explanation_zh":"結構深度核對=([9, 8, 5, -1], linfinity, 9)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262047,"parameters":{"vector":[9,8,5,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[9,8,5,-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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0048","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[10,0,-7,0]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([10, 0, -7, 0], linfinity, 10)","explanation_zh":"結構深度核對=([10, 0, -7, 0], linfinity, 10)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262048,"parameters":{"vector":[10,0,-7,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[10,0,-7,0]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0049","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[11,-6,0,1]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([11, -6, 0, 1], linfinity, 11)","explanation_zh":"結構深度核對=([11, -6, 0, 1], linfinity, 11)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262049,"parameters":{"vector":[11,-6,0,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[11,-6,0,1]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0050","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-linfinity-evaluate；資料={\"vector\":[12,7,7,2]}。請依 [vector,norm_name,value] 欄序回答。","answer":{"kind":"expression","value":"([12, 7, 7, 2], linfinity, 12)","explanation_zh":"結構深度核對=([12, 7, 7, 2], linfinity, 12)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-linfinity-evaluate","seed":202610262050,"parameters":{"vector":[12,7,7,2],"domain":"Named_exact_norms_on_Rn","operation":"norm-linfinity-evaluate","semantic_template":"qf-mod26-norm-linfinity-evaluate/{\"vector\":[12,7,7,2]}"}},"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、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0051","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":1}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 1, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 1, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262051,"parameters":{"norm_name":"l1","dimension":1,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":1,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0052","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":2}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 2, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 2, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262052,"parameters":{"norm_name":"linfinity","dimension":2,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":2,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0053","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":3}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 3, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 3, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262053,"parameters":{"norm_name":"l1","dimension":3,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":3,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0054","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":4}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 4, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 4, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262054,"parameters":{"norm_name":"linfinity","dimension":4,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":4,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0055","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":5}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 5, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 5, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262055,"parameters":{"norm_name":"l1","dimension":5,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":5,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0056","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":6}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 6, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 6, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262056,"parameters":{"norm_name":"linfinity","dimension":6,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":6,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0057","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":7}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 7, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 7, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262057,"parameters":{"norm_name":"l1","dimension":7,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":7,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0058","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":8}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 8, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 8, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262058,"parameters":{"norm_name":"linfinity","dimension":8,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":8,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0059","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":9}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 9, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 9, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262059,"parameters":{"norm_name":"l1","dimension":9,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":9,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0060","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":10}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 10, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 10, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262060,"parameters":{"norm_name":"linfinity","dimension":10,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":10,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0061","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":11}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 11, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 11, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262061,"parameters":{"norm_name":"l1","dimension":11,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":11,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0062","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":12}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 12, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 12, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262062,"parameters":{"norm_name":"linfinity","dimension":12,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":12,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0063","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":13}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 13, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 13, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262063,"parameters":{"norm_name":"l1","dimension":13,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":13,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0064","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":14}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 14, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 14, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262064,"parameters":{"norm_name":"linfinity","dimension":14,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":14,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0065","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":15}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 15, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 15, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262065,"parameters":{"norm_name":"l1","dimension":15,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":15,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0066","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":16}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 16, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 16, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262066,"parameters":{"norm_name":"linfinity","dimension":16,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":16,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0067","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":17}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 17, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 17, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262067,"parameters":{"norm_name":"l1","dimension":17,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":17,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0068","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":18}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 18, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 18, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262068,"parameters":{"norm_name":"linfinity","dimension":18,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":18,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0069","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":19}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 19, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 19, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262069,"parameters":{"norm_name":"l1","dimension":19,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":19,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0070","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":20}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 20, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 20, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262070,"parameters":{"norm_name":"linfinity","dimension":20,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":20,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0071","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":21}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 21, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 21, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262071,"parameters":{"norm_name":"l1","dimension":21,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":21,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0072","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":22}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 22, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 22, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262072,"parameters":{"norm_name":"linfinity","dimension":22,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":22,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0073","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":23}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 23, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 23, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262073,"parameters":{"norm_name":"l1","dimension":23,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":23,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0074","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"linfinity\",\"dimension\":24}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 24, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(linfinity, 24, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262074,"parameters":{"norm_name":"linfinity","dimension":24,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":24,\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0075","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-named-norm-certificate；資料={\"norm_name\":\"l1\",\"dimension\":25}。請依 [norm_name,dimension,qualified,universal_certificate,evidence_mode] 欄序回答。","answer":{"kind":"expression","value":"(l1, 25, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)","explanation_zh":"結構深度核對=(l1, 25, 是, positivity+absolute_homogeneity+triangle_inequality_by_named_formula, not_sampled)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-named-norm-certificate","seed":202610262075,"parameters":{"norm_name":"l1","dimension":25,"domain":"Named_exact_norms_on_Rn","operation":"norm-named-norm-certificate","semantic_template":"qf-mod26-norm-named-norm-certificate/{\"dimension\":25,\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0076","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[-12,-3,-5],\"right\":[12,-6,-2]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-12, -3, -5], [12, -6, -2], [-24, 3, -3], 30)","explanation_zh":"結構深度核對=(l1, [-12, -3, -5], [12, -6, -2], [-24, 3, -3], 30)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262076,"parameters":{"norm_name":"l1","left":[-12,-3,-5],"right":[12,-6,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-12,-3,-5],\"norm_name\":\"l1\",\"right\":[12,-6,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0077","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[-11,-2,-2],\"right\":[11,-1,-1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-11, -2, -2], [11, -1, -1], [-22, -1, -1], 22)","explanation_zh":"結構深度核對=(linfinity, [-11, -2, -2], [11, -1, -1], [-22, -1, -1], 22)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262077,"parameters":{"norm_name":"linfinity","left":[-11,-2,-2],"right":[11,-1,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-11,-2,-2],\"norm_name\":\"linfinity\",\"right\":[11,-1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0078","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[-10,-1,1],\"right\":[10,4,0]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-10, -1, 1], [10, 4, 0], [-20, -5, 1], 26)","explanation_zh":"結構深度核對=(l1, [-10, -1, 1], [10, 4, 0], [-20, -5, 1], 26)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262078,"parameters":{"norm_name":"l1","left":[-10,-1,1],"right":[10,4,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-10,-1,1],\"norm_name\":\"l1\",\"right\":[10,4,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0079","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[-9,0,4],\"right\":[9,-4,1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-9, 0, 4], [9, -4, 1], [-18, 4, 3], 18)","explanation_zh":"結構深度核對=(linfinity, [-9, 0, 4], [9, -4, 1], [-18, 4, 3], 18)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262079,"parameters":{"norm_name":"linfinity","left":[-9,0,4],"right":[9,-4,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-9,0,4],\"norm_name\":\"linfinity\",\"right\":[9,-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0080","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[-8,1,-4],\"right\":[8,1,-2]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-8, 1, -4], [8, 1, -2], [-16, 0, -2], 18)","explanation_zh":"結構深度核對=(l1, [-8, 1, -4], [8, 1, -2], [-16, 0, -2], 18)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262080,"parameters":{"norm_name":"l1","left":[-8,1,-4],"right":[8,1,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-8,1,-4],\"norm_name\":\"l1\",\"right\":[8,1,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0081","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[-7,2,-1],\"right\":[7,6,-1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-7, 2, -1], [7, 6, -1], [-14, -4, 0], 14)","explanation_zh":"結構深度核對=(linfinity, [-7, 2, -1], [7, 6, -1], [-14, -4, 0], 14)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262081,"parameters":{"norm_name":"linfinity","left":[-7,2,-1],"right":[7,6,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-7,2,-1],\"norm_name\":\"linfinity\",\"right\":[7,6,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0082","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[-6,3,2],\"right\":[6,-2,0]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-6, 3, 2], [6, -2, 0], [-12, 5, 2], 19)","explanation_zh":"結構深度核對=(l1, [-6, 3, 2], [6, -2, 0], [-12, 5, 2], 19)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262082,"parameters":{"norm_name":"l1","left":[-6,3,2],"right":[6,-2,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-6,3,2],\"norm_name\":\"l1\",\"right\":[6,-2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0083","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[-5,-3,5],\"right\":[5,3,1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-5, -3, 5], [5, 3, 1], [-10, -6, 4], 10)","explanation_zh":"結構深度核對=(linfinity, [-5, -3, 5], [5, 3, 1], [-10, -6, 4], 10)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262083,"parameters":{"norm_name":"linfinity","left":[-5,-3,5],"right":[5,3,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-5,-3,5],\"norm_name\":\"linfinity\",\"right\":[5,3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0084","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[-4,-2,-3],\"right\":[4,-5,-2]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-4, -2, -3], [4, -5, -2], [-8, 3, -1], 12)","explanation_zh":"結構深度核對=(l1, [-4, -2, -3], [4, -5, -2], [-8, 3, -1], 12)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262084,"parameters":{"norm_name":"l1","left":[-4,-2,-3],"right":[4,-5,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-4,-2,-3],\"norm_name\":\"l1\",\"right\":[4,-5,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0085","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[-3,-1,0],\"right\":[3,0,-1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-3, -1, 0], [3, 0, -1], [-6, -1, 1], 6)","explanation_zh":"結構深度核對=(linfinity, [-3, -1, 0], [3, 0, -1], [-6, -1, 1], 6)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262085,"parameters":{"norm_name":"linfinity","left":[-3,-1,0],"right":[3,0,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-3,-1,0],\"norm_name\":\"linfinity\",\"right\":[3,0,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0086","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[-2,0,3],\"right\":[2,5,0]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [-2, 0, 3], [2, 5, 0], [-4, -5, 3], 12)","explanation_zh":"結構深度核對=(l1, [-2, 0, 3], [2, 5, 0], [-4, -5, 3], 12)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262086,"parameters":{"norm_name":"l1","left":[-2,0,3],"right":[2,5,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-2,0,3],\"norm_name\":\"l1\",\"right\":[2,5,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0087","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[-1,1,-5],\"right\":[1,-3,1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [-1, 1, -5], [1, -3, 1], [-2, 4, -6], 6)","explanation_zh":"結構深度核對=(linfinity, [-1, 1, -5], [1, -3, 1], [-2, 4, -6], 6)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262087,"parameters":{"norm_name":"linfinity","left":[-1,1,-5],"right":[1,-3,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[-1,1,-5],\"norm_name\":\"linfinity\",\"right\":[1,-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0088","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[0,2,-2],\"right\":[0,2,-2]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [0, 2, -2], [0, 2, -2], [0, 0, 0], 0)","explanation_zh":"結構深度核對=(l1, [0, 2, -2], [0, 2, -2], [0, 0, 0], 0)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262088,"parameters":{"norm_name":"l1","left":[0,2,-2],"right":[0,2,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[0,2,-2],\"norm_name\":\"l1\",\"right\":[0,2,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0089","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[1,3,1],\"right\":[-1,-6,-1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [1, 3, 1], [-1, -6, -1], [2, 9, 2], 9)","explanation_zh":"結構深度核對=(linfinity, [1, 3, 1], [-1, -6, -1], [2, 9, 2], 9)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262089,"parameters":{"norm_name":"linfinity","left":[1,3,1],"right":[-1,-6,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[1,3,1],\"norm_name\":\"linfinity\",\"right\":[-1,-6,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0090","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[2,-3,4],\"right\":[-2,-1,0]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [2, -3, 4], [-2, -1, 0], [4, -2, 4], 10)","explanation_zh":"結構深度核對=(l1, [2, -3, 4], [-2, -1, 0], [4, -2, 4], 10)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262090,"parameters":{"norm_name":"l1","left":[2,-3,4],"right":[-2,-1,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[2,-3,4],\"norm_name\":\"l1\",\"right\":[-2,-1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0091","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[3,-2,-4],\"right\":[-3,4,1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [3, -2, -4], [-3, 4, 1], [6, -6, -5], 6)","explanation_zh":"結構深度核對=(linfinity, [3, -2, -4], [-3, 4, 1], [6, -6, -5], 6)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262091,"parameters":{"norm_name":"linfinity","left":[3,-2,-4],"right":[-3,4,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[3,-2,-4],\"norm_name\":\"linfinity\",\"right\":[-3,4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0092","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[4,-1,-1],\"right\":[-4,-4,-2]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [4, -1, -1], [-4, -4, -2], [8, 3, 1], 12)","explanation_zh":"結構深度核對=(l1, [4, -1, -1], [-4, -4, -2], [8, 3, 1], 12)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262092,"parameters":{"norm_name":"l1","left":[4,-1,-1],"right":[-4,-4,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[4,-1,-1],\"norm_name\":\"l1\",\"right\":[-4,-4,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0093","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[5,0,2],\"right\":[-5,1,-1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [5, 0, 2], [-5, 1, -1], [10, -1, 3], 10)","explanation_zh":"結構深度核對=(linfinity, [5, 0, 2], [-5, 1, -1], [10, -1, 3], 10)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262093,"parameters":{"norm_name":"linfinity","left":[5,0,2],"right":[-5,1,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[5,0,2],\"norm_name\":\"linfinity\",\"right\":[-5,1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0094","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[6,1,5],\"right\":[-6,6,0]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [6, 1, 5], [-6, 6, 0], [12, -5, 5], 22)","explanation_zh":"結構深度核對=(l1, [6, 1, 5], [-6, 6, 0], [12, -5, 5], 22)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262094,"parameters":{"norm_name":"l1","left":[6,1,5],"right":[-6,6,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[6,1,5],\"norm_name\":\"l1\",\"right\":[-6,6,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0095","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[7,2,-3],\"right\":[-7,-2,1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [7, 2, -3], [-7, -2, 1], [14, 4, -4], 14)","explanation_zh":"結構深度核對=(linfinity, [7, 2, -3], [-7, -2, 1], [14, 4, -4], 14)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262095,"parameters":{"norm_name":"linfinity","left":[7,2,-3],"right":[-7,-2,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[7,2,-3],\"norm_name\":\"linfinity\",\"right\":[-7,-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0096","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[8,3,0],\"right\":[-8,3,-2]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [8, 3, 0], [-8, 3, -2], [16, 0, 2], 18)","explanation_zh":"結構深度核對=(l1, [8, 3, 0], [-8, 3, -2], [16, 0, 2], 18)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262096,"parameters":{"norm_name":"l1","left":[8,3,0],"right":[-8,3,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[8,3,0],\"norm_name\":\"l1\",\"right\":[-8,3,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0097","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[9,-3,3],\"right\":[-9,-5,-1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [9, -3, 3], [-9, -5, -1], [18, 2, 4], 18)","explanation_zh":"結構深度核對=(linfinity, [9, -3, 3], [-9, -5, -1], [18, 2, 4], 18)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262097,"parameters":{"norm_name":"linfinity","left":[9,-3,3],"right":[-9,-5,-1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[9,-3,3],\"norm_name\":\"linfinity\",\"right\":[-9,-5,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0098","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[10,-2,-5],\"right\":[-10,0,0]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [10, -2, -5], [-10, 0, 0], [20, -2, -5], 27)","explanation_zh":"結構深度核對=(l1, [10, -2, -5], [-10, 0, 0], [20, -2, -5], 27)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262098,"parameters":{"norm_name":"l1","left":[10,-2,-5],"right":[-10,0,0],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[10,-2,-5],\"norm_name\":\"l1\",\"right\":[-10,0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0099","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"linfinity\",\"left\":[11,-1,-2],\"right\":[-11,5,1]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, [11, -1, -2], [-11, 5, 1], [22, -6, -3], 22)","explanation_zh":"結構深度核對=(linfinity, [11, -1, -2], [-11, 5, 1], [22, -6, -3], 22)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262099,"parameters":{"norm_name":"linfinity","left":[11,-1,-2],"right":[-11,5,1],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[11,-1,-2],\"norm_name\":\"linfinity\",\"right\":[-11,5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r02-real-normed-vector-space-0100","batch_id":"batch-20261013-advance-20261026-r02-real-normed-vector-space-foundations","language":"zh-Hant","source_mko_ids":["mko-real-normed-vector-space"],"title_zh":"實賦範向量空間","stem_zh":"只使用明示l1或linfinity精確公式。操作=norm-induced-distance；資料={\"norm_name\":\"l1\",\"left\":[12,0,1],\"right\":[-12,-3,-2]}。請依 [norm_name,left,right,difference,distance] 欄序回答。","answer":{"kind":"expression","value":"(l1, [12, 0, 1], [-12, -3, -2], [24, 3, 3], 30)","explanation_zh":"結構深度核對=(l1, [12, 0, 1], [-12, -3, -2], [24, 3, 3], 30)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；命名公式提供全稱代數證書；有限點抽樣不能證範數公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["實賦範向量空間"]},"variant":{"family_id":"qf-mod26-norm-induced-distance","seed":202610262100,"parameters":{"norm_name":"l1","left":[12,0,1],"right":[-12,-3,-2],"domain":"Named_exact_norms_on_Rn","operation":"norm-induced-distance","semantic_template":"qf-mod26-norm-induced-distance/{\"left\":[12,0,1],\"norm_name\":\"l1\",\"right\":[-12,-3,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}