{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0001","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [-12, -3, -5], [12, -6, -2], [-24, 3, -3], 30)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272001,"parameters":{"norm_name":"l1","left":[-12,-3,-5],"right":[12,-6,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0002","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [-11, -2, -2], [11, -1, -1], [-22, -1, -1], 22)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272002,"parameters":{"norm_name":"linfinity","left":[-11,-2,-2],"right":[11,-1,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0003","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [-10, -1, 1], [10, 4, 0], [-20, -5, 1], 26)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272003,"parameters":{"norm_name":"l1","left":[-10,-1,1],"right":[10,4,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0004","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [-9, 0, 4], [9, -4, 1], [-18, 4, 3], 18)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272004,"parameters":{"norm_name":"linfinity","left":[-9,0,4],"right":[9,-4,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0005","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [-8, 1, -4], [8, 1, -2], [-16, 0, -2], 18)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272005,"parameters":{"norm_name":"l1","left":[-8,1,-4],"right":[8,1,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0006","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [-7, 2, -1], [7, 6, -1], [-14, -4, 0], 14)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272006,"parameters":{"norm_name":"linfinity","left":[-7,2,-1],"right":[7,6,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0007","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [-6, 3, 2], [6, -2, 0], [-12, 5, 2], 19)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272007,"parameters":{"norm_name":"l1","left":[-6,3,2],"right":[6,-2,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0008","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [-5, -3, 5], [5, 3, 1], [-10, -6, 4], 10)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272008,"parameters":{"norm_name":"linfinity","left":[-5,-3,5],"right":[5,3,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0009","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [-4, -2, -3], [4, -5, -2], [-8, 3, -1], 12)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272009,"parameters":{"norm_name":"l1","left":[-4,-2,-3],"right":[4,-5,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0010","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [-3, -1, 0], [3, 0, -1], [-6, -1, 1], 6)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272010,"parameters":{"norm_name":"linfinity","left":[-3,-1,0],"right":[3,0,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0011","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [-2, 0, 3], [2, 5, 0], [-4, -5, 3], 12)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272011,"parameters":{"norm_name":"l1","left":[-2,0,3],"right":[2,5,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0012","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [-1, 1, -5], [1, -3, 1], [-2, 4, -6], 6)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272012,"parameters":{"norm_name":"linfinity","left":[-1,1,-5],"right":[1,-3,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0013","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [0, 2, -2], [0, 2, -2], [0, 0, 0], 0)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272013,"parameters":{"norm_name":"l1","left":[0,2,-2],"right":[0,2,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0014","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [1, 3, 1], [-1, -6, -1], [2, 9, 2], 9)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272014,"parameters":{"norm_name":"linfinity","left":[1,3,1],"right":[-1,-6,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0015","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [2, -3, 4], [-2, -1, 0], [4, -2, 4], 10)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272015,"parameters":{"norm_name":"l1","left":[2,-3,4],"right":[-2,-1,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0016","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [3, -2, -4], [-3, 4, 1], [6, -6, -5], 6)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272016,"parameters":{"norm_name":"linfinity","left":[3,-2,-4],"right":[-3,4,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0017","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [4, -1, -1], [-4, -4, -2], [8, 3, 1], 12)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272017,"parameters":{"norm_name":"l1","left":[4,-1,-1],"right":[-4,-4,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0018","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [5, 0, 2], [-5, 1, -1], [10, -1, 3], 10)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272018,"parameters":{"norm_name":"linfinity","left":[5,0,2],"right":[-5,1,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0019","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [6, 1, 5], [-6, 6, 0], [12, -5, 5], 22)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272019,"parameters":{"norm_name":"l1","left":[6,1,5],"right":[-6,6,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0020","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [7, 2, -3], [-7, -2, 1], [14, 4, -4], 14)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272020,"parameters":{"norm_name":"linfinity","left":[7,2,-3],"right":[-7,-2,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0021","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [8, 3, 0], [-8, 3, -2], [16, 0, 2], 18)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272021,"parameters":{"norm_name":"l1","left":[8,3,0],"right":[-8,3,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0022","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [9, -3, 3], [-9, -5, -1], [18, 2, 4], 18)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272022,"parameters":{"norm_name":"linfinity","left":[9,-3,3],"right":[-9,-5,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0023","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [10, -2, -5], [-10, 0, 0], [20, -2, -5], 27)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272023,"parameters":{"norm_name":"l1","left":[10,-2,-5],"right":[-10,0,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0024","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(linfinity, [11, -1, -2], [-11, 5, 1], [22, -6, -3], 22)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272024,"parameters":{"norm_name":"linfinity","left":[11,-1,-2],"right":[-11,5,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0025","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-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":"Wave4根節點核對=(l1, [12, 0, 1], [-12, -3, -2], [24, 3, 3], 30)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-distance","seed":202610272025,"parameters":{"norm_name":"l1","left":[12,0,1],"right":[-12,-3,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-distance","semantic_template":"qf-mod27-normmetric-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、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0026","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[-12,-3,-5],\"right\":[12,-6,-2]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 30, 30, 是)","explanation_zh":"Wave4根節點核對=(l1, 30, 30, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272026,"parameters":{"norm_name":"l1","left":[-12,-3,-5],"right":[12,-6,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-12,-3,-5],\"norm_name\":\"l1\",\"right\":[12,-6,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0027","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[-11,-2,-2],\"right\":[11,-1,-1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 22, 22, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 22, 22, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272027,"parameters":{"norm_name":"linfinity","left":[-11,-2,-2],"right":[11,-1,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-11,-2,-2],\"norm_name\":\"linfinity\",\"right\":[11,-1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0028","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[-10,-1,1],\"right\":[10,4,0]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 26, 26, 是)","explanation_zh":"Wave4根節點核對=(l1, 26, 26, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272028,"parameters":{"norm_name":"l1","left":[-10,-1,1],"right":[10,4,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-10,-1,1],\"norm_name\":\"l1\",\"right\":[10,4,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0029","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[-9,0,4],\"right\":[9,-4,1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 18, 18, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 18, 18, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272029,"parameters":{"norm_name":"linfinity","left":[-9,0,4],"right":[9,-4,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-9,0,4],\"norm_name\":\"linfinity\",\"right\":[9,-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0030","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[-8,1,-4],\"right\":[8,1,-2]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 18, 18, 是)","explanation_zh":"Wave4根節點核對=(l1, 18, 18, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272030,"parameters":{"norm_name":"l1","left":[-8,1,-4],"right":[8,1,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-8,1,-4],\"norm_name\":\"l1\",\"right\":[8,1,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0031","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[-7,2,-1],\"right\":[7,6,-1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 14, 14, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 14, 14, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272031,"parameters":{"norm_name":"linfinity","left":[-7,2,-1],"right":[7,6,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-7,2,-1],\"norm_name\":\"linfinity\",\"right\":[7,6,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0032","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[-6,3,2],\"right\":[6,-2,0]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 19, 19, 是)","explanation_zh":"Wave4根節點核對=(l1, 19, 19, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272032,"parameters":{"norm_name":"l1","left":[-6,3,2],"right":[6,-2,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-6,3,2],\"norm_name\":\"l1\",\"right\":[6,-2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0033","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[-5,-3,5],\"right\":[5,3,1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 10, 10, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 10, 10, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272033,"parameters":{"norm_name":"linfinity","left":[-5,-3,5],"right":[5,3,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-5,-3,5],\"norm_name\":\"linfinity\",\"right\":[5,3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0034","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[-4,-2,-3],\"right\":[4,-5,-2]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 12, 12, 是)","explanation_zh":"Wave4根節點核對=(l1, 12, 12, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272034,"parameters":{"norm_name":"l1","left":[-4,-2,-3],"right":[4,-5,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-4,-2,-3],\"norm_name\":\"l1\",\"right\":[4,-5,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0035","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[-3,-1,0],\"right\":[3,0,-1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 6, 6, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 6, 6, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272035,"parameters":{"norm_name":"linfinity","left":[-3,-1,0],"right":[3,0,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-3,-1,0],\"norm_name\":\"linfinity\",\"right\":[3,0,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0036","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[-2,0,3],\"right\":[2,5,0]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 12, 12, 是)","explanation_zh":"Wave4根節點核對=(l1, 12, 12, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272036,"parameters":{"norm_name":"l1","left":[-2,0,3],"right":[2,5,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-2,0,3],\"norm_name\":\"l1\",\"right\":[2,5,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0037","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[-1,1,-5],\"right\":[1,-3,1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 6, 6, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 6, 6, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272037,"parameters":{"norm_name":"linfinity","left":[-1,1,-5],"right":[1,-3,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[-1,1,-5],\"norm_name\":\"linfinity\",\"right\":[1,-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0038","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[0,2,-2],\"right\":[0,2,-2]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 0, 0, 是)","explanation_zh":"Wave4根節點核對=(l1, 0, 0, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272038,"parameters":{"norm_name":"l1","left":[0,2,-2],"right":[0,2,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[0,2,-2],\"norm_name\":\"l1\",\"right\":[0,2,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0039","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[1,3,1],\"right\":[-1,-6,-1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 9, 9, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 9, 9, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272039,"parameters":{"norm_name":"linfinity","left":[1,3,1],"right":[-1,-6,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[1,3,1],\"norm_name\":\"linfinity\",\"right\":[-1,-6,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0040","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[2,-3,4],\"right\":[-2,-1,0]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 10, 10, 是)","explanation_zh":"Wave4根節點核對=(l1, 10, 10, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272040,"parameters":{"norm_name":"l1","left":[2,-3,4],"right":[-2,-1,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[2,-3,4],\"norm_name\":\"l1\",\"right\":[-2,-1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0041","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[3,-2,-4],\"right\":[-3,4,1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 6, 6, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 6, 6, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272041,"parameters":{"norm_name":"linfinity","left":[3,-2,-4],"right":[-3,4,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[3,-2,-4],\"norm_name\":\"linfinity\",\"right\":[-3,4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0042","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[4,-1,-1],\"right\":[-4,-4,-2]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 12, 12, 是)","explanation_zh":"Wave4根節點核對=(l1, 12, 12, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272042,"parameters":{"norm_name":"l1","left":[4,-1,-1],"right":[-4,-4,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[4,-1,-1],\"norm_name\":\"l1\",\"right\":[-4,-4,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0043","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[5,0,2],\"right\":[-5,1,-1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 10, 10, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 10, 10, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272043,"parameters":{"norm_name":"linfinity","left":[5,0,2],"right":[-5,1,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[5,0,2],\"norm_name\":\"linfinity\",\"right\":[-5,1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0044","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[6,1,5],\"right\":[-6,6,0]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 22, 22, 是)","explanation_zh":"Wave4根節點核對=(l1, 22, 22, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272044,"parameters":{"norm_name":"l1","left":[6,1,5],"right":[-6,6,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[6,1,5],\"norm_name\":\"l1\",\"right\":[-6,6,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0045","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[7,2,-3],\"right\":[-7,-2,1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 14, 14, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 14, 14, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272045,"parameters":{"norm_name":"linfinity","left":[7,2,-3],"right":[-7,-2,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[7,2,-3],\"norm_name\":\"linfinity\",\"right\":[-7,-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0046","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[8,3,0],\"right\":[-8,3,-2]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 18, 18, 是)","explanation_zh":"Wave4根節點核對=(l1, 18, 18, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272046,"parameters":{"norm_name":"l1","left":[8,3,0],"right":[-8,3,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[8,3,0],\"norm_name\":\"l1\",\"right\":[-8,3,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0047","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[9,-3,3],\"right\":[-9,-5,-1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 18, 18, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 18, 18, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272047,"parameters":{"norm_name":"linfinity","left":[9,-3,3],"right":[-9,-5,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[9,-3,3],\"norm_name\":\"linfinity\",\"right\":[-9,-5,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0048","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[10,-2,-5],\"right\":[-10,0,0]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 27, 27, 是)","explanation_zh":"Wave4根節點核對=(l1, 27, 27, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272048,"parameters":{"norm_name":"l1","left":[10,-2,-5],"right":[-10,0,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[10,-2,-5],\"norm_name\":\"l1\",\"right\":[-10,0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0049","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"linfinity\",\"left\":[11,-1,-2],\"right\":[-11,5,1]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 22, 22, 是)","explanation_zh":"Wave4根節點核對=(linfinity, 22, 22, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272049,"parameters":{"norm_name":"linfinity","left":[11,-1,-2],"right":[-11,5,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[11,-1,-2],\"norm_name\":\"linfinity\",\"right\":[-11,5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0050","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-symmetry；資料={\"norm_name\":\"l1\",\"left\":[12,0,1],\"right\":[-12,-3,-2]}。請依 [norm_name,d_xy,d_yx,equal] 欄序回答。","answer":{"kind":"expression","value":"(l1, 30, 30, 是)","explanation_zh":"Wave4根節點核對=(l1, 30, 30, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-symmetry","seed":202610272050,"parameters":{"norm_name":"l1","left":[12,0,1],"right":[-12,-3,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-symmetry","semantic_template":"qf-mod27-normmetric-symmetry/{\"left\":[12,0,1],\"norm_name\":\"l1\",\"right\":[-12,-3,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0051","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[-12,-3],\"y\":[-4,12],\"z\":[-6,-2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 7, 23, 16, 39, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 7, 23, 16, 39, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272051,"parameters":{"norm_name":"l1","x":[-12,-3],"y":[-4,12],"z":[-6,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[-12,-3],\"y\":[-4,12],\"z\":[-6,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0052","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[-11,-2],\"y\":[-3,11],\"z\":[-1,-1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 10, 13, 12, 25, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 10, 13, 12, 25, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272052,"parameters":{"norm_name":"linfinity","x":[-11,-2],"y":[-3,11],"z":[-1,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[-11,-2],\"y\":[-3,11],\"z\":[-1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0053","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[-10,-1],\"y\":[-2,10],\"z\":[4,0]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 15, 19, 16, 35, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 15, 19, 16, 35, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272053,"parameters":{"norm_name":"l1","x":[-10,-1],"y":[-2,10],"z":[4,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[-10,-1],\"y\":[-2,10],\"z\":[4,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0054","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[-9,0],\"y\":[-1,9],\"z\":[-4,1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 5, 9, 8, 17, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 5, 9, 8, 17, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272054,"parameters":{"norm_name":"linfinity","x":[-9,0],"y":[-1,9],"z":[-4,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[-9,0],\"y\":[-1,9],\"z\":[-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0055","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[-8,1],\"y\":[0,8],\"z\":[1,2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 10, 15, 7, 22, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 10, 15, 7, 22, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272055,"parameters":{"norm_name":"l1","x":[-8,1],"y":[0,8],"z":[1,2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[-8,1],\"y\":[0,8],\"z\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0056","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[-7,2],\"y\":[1,7],\"z\":[6,-2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 13, 8, 9, 17, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 13, 8, 9, 17, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272056,"parameters":{"norm_name":"linfinity","x":[-7,2],"y":[1,7],"z":[6,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[-7,2],\"y\":[1,7],\"z\":[6,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0057","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[-6,3],\"y\":[2,6],\"z\":[-2,-1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 8, 11, 11, 22, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 8, 11, 11, 22, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272057,"parameters":{"norm_name":"l1","x":[-6,3],"y":[2,6],"z":[-2,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[-6,3],\"y\":[2,6],\"z\":[-2,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0058","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[-5,-3],\"y\":[3,5],\"z\":[3,0]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 8, 8, 5, 13, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 8, 8, 5, 13, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272058,"parameters":{"norm_name":"linfinity","x":[-5,-3],"y":[3,5],"z":[3,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[-5,-3],\"y\":[3,5],\"z\":[3,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0059","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[-4,-2],\"y\":[4,4],\"z\":[-5,1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 4, 14, 12, 26, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 4, 14, 12, 26, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272059,"parameters":{"norm_name":"l1","x":[-4,-2],"y":[4,4],"z":[-5,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[-4,-2],\"y\":[4,4],\"z\":[-5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0060","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[-3,-1],\"y\":[-4,3],\"z\":[0,2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 3, 4, 4, 8, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 3, 4, 4, 8, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272060,"parameters":{"norm_name":"linfinity","x":[-3,-1],"y":[-4,3],"z":[0,2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[-3,-1],\"y\":[-4,3],\"z\":[0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0061","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[-2,0],\"y\":[-3,2],\"z\":[5,-2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 9, 3, 12, 15, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 9, 3, 12, 15, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272061,"parameters":{"norm_name":"l1","x":[-2,0],"y":[-3,2],"z":[5,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[-2,0],\"y\":[-3,2],\"z\":[5,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0062","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[-1,1],\"y\":[-2,1],\"z\":[-3,-1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 2, 1, 2, 3, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 2, 1, 2, 3, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272062,"parameters":{"norm_name":"linfinity","x":[-1,1],"y":[-2,1],"z":[-3,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[-1,1],\"y\":[-2,1],\"z\":[-3,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0063","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[0,2],\"y\":[-1,0],\"z\":[2,0]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 4, 3, 3, 6, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 4, 3, 3, 6, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272063,"parameters":{"norm_name":"l1","x":[0,2],"y":[-1,0],"z":[2,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[0,2],\"y\":[-1,0],\"z\":[2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0064","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[1,3],\"y\":[0,-1],\"z\":[-6,1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 7, 4, 6, 10, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 7, 4, 6, 10, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272064,"parameters":{"norm_name":"linfinity","x":[1,3],"y":[0,-1],"z":[-6,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[1,3],\"y\":[0,-1],\"z\":[-6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0065","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[2,-3],\"y\":[1,-2],\"z\":[-1,2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 8, 2, 6, 8, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 8, 2, 6, 8, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272065,"parameters":{"norm_name":"l1","x":[2,-3],"y":[1,-2],"z":[-1,2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[2,-3],\"y\":[1,-2],\"z\":[-1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0066","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[3,-2],\"y\":[2,-3],\"z\":[4,-2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 1, 1, 2, 3, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 1, 1, 2, 3, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272066,"parameters":{"norm_name":"linfinity","x":[3,-2],"y":[2,-3],"z":[4,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[3,-2],\"y\":[2,-3],\"z\":[4,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0067","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[4,-1],\"y\":[3,-4],\"z\":[-4,-1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 8, 4, 10, 14, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 8, 4, 10, 14, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272067,"parameters":{"norm_name":"l1","x":[4,-1],"y":[3,-4],"z":[-4,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[4,-1],\"y\":[3,-4],\"z\":[-4,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0068","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[5,0],\"y\":[4,-5],\"z\":[1,0]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 4, 5, 5, 10, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 4, 5, 5, 10, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272068,"parameters":{"norm_name":"linfinity","x":[5,0],"y":[4,-5],"z":[1,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[5,0],\"y\":[4,-5],\"z\":[1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0069","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[6,1],\"y\":[-4,-6],\"z\":[6,1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 0, 17, 17, 34, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 0, 17, 17, 34, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272069,"parameters":{"norm_name":"l1","x":[6,1],"y":[-4,-6],"z":[6,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[6,1],\"y\":[-4,-6],\"z\":[6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0070","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[7,2],\"y\":[-3,-7],\"z\":[-2,2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 9, 10, 9, 19, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 9, 10, 9, 19, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272070,"parameters":{"norm_name":"linfinity","x":[7,2],"y":[-3,-7],"z":[-2,2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[7,2],\"y\":[-3,-7],\"z\":[-2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0071","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[8,3],\"y\":[-2,-8],\"z\":[3,-2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 10, 21, 11, 32, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 10, 21, 11, 32, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272071,"parameters":{"norm_name":"l1","x":[8,3],"y":[-2,-8],"z":[3,-2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[8,3],\"y\":[-2,-8],\"z\":[3,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0072","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[9,-3],\"y\":[-1,-9],\"z\":[-5,-1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 14, 10, 8, 18, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 14, 10, 8, 18, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272072,"parameters":{"norm_name":"linfinity","x":[9,-3],"y":[-1,-9],"z":[-5,-1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[9,-3],\"y\":[-1,-9],\"z\":[-5,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0073","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[10,-2],\"y\":[0,-10],\"z\":[0,0]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 12, 18, 10, 28, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 12, 18, 10, 28, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272073,"parameters":{"norm_name":"l1","x":[10,-2],"y":[0,-10],"z":[0,0],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[10,-2],\"y\":[0,-10],\"z\":[0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0074","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"linfinity\",\"x\":[11,-1],\"y\":[1,-11],\"z\":[5,1]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 6, 10, 12, 22, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(linfinity, 6, 10, 12, 22, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272074,"parameters":{"norm_name":"linfinity","x":[11,-1],"y":[1,-11],"z":[5,1],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"linfinity\",\"x\":[11,-1],\"y\":[1,-11],\"z\":[5,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0075","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-triangle-certificate；資料={\"norm_name\":\"l1\",\"x\":[12,0],\"y\":[2,-12],\"z\":[-3,2]}。請依 [norm_name,d_xz,d_xy,d_yz,rhs,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(l1, 17, 22, 19, 41, 是, norm_triangle_inequality)","explanation_zh":"Wave4根節點核對=(l1, 17, 22, 19, 41, 是, norm_triangle_inequality)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-triangle-certificate","seed":202610272075,"parameters":{"norm_name":"l1","x":[12,0],"y":[2,-12],"z":[-3,2],"domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-triangle-certificate","semantic_template":"qf-mod27-normmetric-triangle-certificate/{\"norm_name\":\"l1\",\"x\":[12,0],\"y\":[2,-12],\"z\":[-3,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0076","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":1,\"evidence_mode\":\"finite_samples\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 1, finite_samples, 否, samples_do_not_establish_induced_metric)","explanation_zh":"Wave4根節點核對=(l1, 1, finite_samples, 否, samples_do_not_establish_induced_metric)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272076,"parameters":{"norm_name":"l1","dimension":1,"evidence_mode":"finite_samples","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":1,\"evidence_mode\":\"finite_samples\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0077","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":2,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 2, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 2, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272077,"parameters":{"norm_name":"linfinity","dimension":2,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":2,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0078","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":3,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 3, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(l1, 3, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272078,"parameters":{"norm_name":"l1","dimension":3,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":3,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0079","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":4,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 4, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 4, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272079,"parameters":{"norm_name":"linfinity","dimension":4,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":4,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0080","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":5,\"evidence_mode\":\"finite_samples\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 5, finite_samples, 否, samples_do_not_establish_induced_metric)","explanation_zh":"Wave4根節點核對=(l1, 5, finite_samples, 否, samples_do_not_establish_induced_metric)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272080,"parameters":{"norm_name":"l1","dimension":5,"evidence_mode":"finite_samples","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":5,\"evidence_mode\":\"finite_samples\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0081","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":6,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 6, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 6, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272081,"parameters":{"norm_name":"linfinity","dimension":6,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":6,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0082","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":7,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 7, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(l1, 7, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272082,"parameters":{"norm_name":"l1","dimension":7,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":7,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0083","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":8,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 8, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 8, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272083,"parameters":{"norm_name":"linfinity","dimension":8,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":8,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0084","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":9,\"evidence_mode\":\"finite_samples\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 9, finite_samples, 否, samples_do_not_establish_induced_metric)","explanation_zh":"Wave4根節點核對=(l1, 9, finite_samples, 否, samples_do_not_establish_induced_metric)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272084,"parameters":{"norm_name":"l1","dimension":9,"evidence_mode":"finite_samples","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":9,\"evidence_mode\":\"finite_samples\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0085","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":10,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 10, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 10, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272085,"parameters":{"norm_name":"linfinity","dimension":10,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":10,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0086","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":11,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 11, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(l1, 11, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272086,"parameters":{"norm_name":"l1","dimension":11,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":11,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0087","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":12,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 12, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 12, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272087,"parameters":{"norm_name":"linfinity","dimension":12,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":12,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0088","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":13,\"evidence_mode\":\"finite_samples\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 13, finite_samples, 否, samples_do_not_establish_induced_metric)","explanation_zh":"Wave4根節點核對=(l1, 13, finite_samples, 否, samples_do_not_establish_induced_metric)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272088,"parameters":{"norm_name":"l1","dimension":13,"evidence_mode":"finite_samples","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":13,\"evidence_mode\":\"finite_samples\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0089","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":14,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 14, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 14, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272089,"parameters":{"norm_name":"linfinity","dimension":14,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":14,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0090","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":15,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 15, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(l1, 15, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272090,"parameters":{"norm_name":"l1","dimension":15,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":15,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0091","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":16,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 16, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 16, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272091,"parameters":{"norm_name":"linfinity","dimension":16,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":16,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0092","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":17,\"evidence_mode\":\"finite_samples\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 17, finite_samples, 否, samples_do_not_establish_induced_metric)","explanation_zh":"Wave4根節點核對=(l1, 17, finite_samples, 否, samples_do_not_establish_induced_metric)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272092,"parameters":{"norm_name":"l1","dimension":17,"evidence_mode":"finite_samples","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":17,\"evidence_mode\":\"finite_samples\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0093","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":18,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 18, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 18, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272093,"parameters":{"norm_name":"linfinity","dimension":18,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":18,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0094","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":19,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 19, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(l1, 19, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272094,"parameters":{"norm_name":"l1","dimension":19,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":19,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0095","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":20,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 20, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 20, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272095,"parameters":{"norm_name":"linfinity","dimension":20,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":20,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0096","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":21,\"evidence_mode\":\"finite_samples\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 21, finite_samples, 否, samples_do_not_establish_induced_metric)","explanation_zh":"Wave4根節點核對=(l1, 21, finite_samples, 否, samples_do_not_establish_induced_metric)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272096,"parameters":{"norm_name":"l1","dimension":21,"evidence_mode":"finite_samples","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":21,\"evidence_mode\":\"finite_samples\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0097","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":22,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 22, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 22, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272097,"parameters":{"norm_name":"linfinity","dimension":22,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":22,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0098","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":23,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 23, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(l1, 23, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272098,"parameters":{"norm_name":"l1","dimension":23,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":23,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0099","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"linfinity\",\"dimension\":24,\"evidence_mode\":\"named_formula_certificate\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(linfinity, 24, named_formula_certificate, 是, universal_from_norm_axioms)","explanation_zh":"Wave4根節點核對=(linfinity, 24, named_formula_certificate, 是, universal_from_norm_axioms)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272099,"parameters":{"norm_name":"linfinity","dimension":24,"evidence_mode":"named_formula_certificate","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":24,\"evidence_mode\":\"named_formula_certificate\",\"norm_name\":\"linfinity\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r02-norm-induced-metric-0100","batch_id":"batch-20261014-advance-20261027-r02-norm-induced-metric-foundations","language":"zh-Hant","source_mko_ids":["mko-norm-induced-metric"],"title_zh":"範數誘導度量","stem_zh":"同一已認證範數以d(x,y)=norm(x-y)定義距離。操作=normmetric-induced-qualification；資料={\"norm_name\":\"l1\",\"dimension\":25,\"evidence_mode\":\"finite_samples\"}。請依 [norm_name,dimension,evidence_mode,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(l1, 25, finite_samples, 否, samples_do_not_establish_induced_metric)","explanation_zh":"Wave4根節點核對=(l1, 25, finite_samples, 否, samples_do_not_establish_induced_metric)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；誘導性來自範數公理的全稱證書；不宣稱每個metric皆由norm誘導或空間完備。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["範數誘導度量"]},"variant":{"family_id":"qf-mod27-normmetric-induced-qualification","seed":202610272100,"parameters":{"norm_name":"l1","dimension":25,"evidence_mode":"finite_samples","domain":"Named_norm_induced_metric_on_Rn","operation":"normmetric-induced-qualification","semantic_template":"qf-mod27-normmetric-induced-qualification/{\"dimension\":25,\"evidence_mode\":\"finite_samples\",\"norm_name\":\"l1\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}