{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0001","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-10,-8,12,0],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-10, -8, 12, 0], [是, 是, 否, 是], [0, 1, 3])","explanation_zh":"應用基礎核對=([-10, -8, 12, 0], [是, 是, 否, 是], [0, 1, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204001,"parameters":{"values":[-10,-8,12,0],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[-10,-8,12,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0002","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-9,-5,11,1],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-9, -5, 11, 1], [是, 否, 是, 是], [0, 2, 3])","explanation_zh":"應用基礎核對=([-9, -5, 11, 1], [是, 否, 是, 是], [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204002,"parameters":{"values":[-9,-5,11,1],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[-9,-5,11,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0003","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-8,-2,10,2],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-8, -2, 10, 2], [是, 是, 是, 是], [0, 1, 2, 3])","explanation_zh":"應用基礎核對=([-8, -2, 10, 2], [是, 是, 是, 是], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204003,"parameters":{"values":[-8,-2,10,2],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[-8,-2,10,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0004","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-7,1,9,3],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-7, 1, 9, 3], [是, 否, 否, 是], [0, 3])","explanation_zh":"應用基礎核對=([-7, 1, 9, 3], [是, 否, 否, 是], [0, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204004,"parameters":{"values":[-7,1,9,3],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,false,true],\"values\":[-7,1,9,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0005","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-6,4,8,4],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-6, 4, 8, 4], [是, 是, 是, 是], [0, 1, 2, 3])","explanation_zh":"應用基礎核對=([-6, 4, 8, 4], [是, 是, 是, 是], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204005,"parameters":{"values":[-6,4,8,4],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[-6,4,8,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0006","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-5,7,7,0],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-5, 7, 7, 0], [是, 否, 是, 是], [0, 2, 3])","explanation_zh":"應用基礎核對=([-5, 7, 7, 0], [是, 否, 是, 是], [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204006,"parameters":{"values":[-5,7,7,0],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[-5,7,7,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0007","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-4,-7,6,1],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-4, -7, 6, 1], [是, 是, 否, 是], [0, 1, 3])","explanation_zh":"應用基礎核對=([-4, -7, 6, 1], [是, 是, 否, 是], [0, 1, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204007,"parameters":{"values":[-4,-7,6,1],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[-4,-7,6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0008","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-3,-4,5,2],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-3, -4, 5, 2], [是, 否, 是, 是], [0, 2, 3])","explanation_zh":"應用基礎核對=([-3, -4, 5, 2], [是, 否, 是, 是], [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204008,"parameters":{"values":[-3,-4,5,2],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[-3,-4,5,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0009","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-2,-1,4,3],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-2, -1, 4, 3], [是, 是, 是, 是], [0, 1, 2, 3])","explanation_zh":"應用基礎核對=([-2, -1, 4, 3], [是, 是, 是, 是], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204009,"parameters":{"values":[-2,-1,4,3],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[-2,-1,4,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0010","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[-1,2,3,4],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2, 3, 4], [是, 否, 否, 是], [0, 3])","explanation_zh":"應用基礎核對=([-1, 2, 3, 4], [是, 否, 否, 是], [0, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204010,"parameters":{"values":[-1,2,3,4],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,false,true],\"values\":[-1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0011","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[0,5,2,0],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([0, 5, 2, 0], [是, 是, 是, 是], [0, 1, 2, 3])","explanation_zh":"應用基礎核對=([0, 5, 2, 0], [是, 是, 是, 是], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204011,"parameters":{"values":[0,5,2,0],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[0,5,2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0012","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[1,8,1,1],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 8, 1, 1], [是, 否, 是, 是], [0, 2, 3])","explanation_zh":"應用基礎核對=([1, 8, 1, 1], [是, 否, 是, 是], [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204012,"parameters":{"values":[1,8,1,1],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[1,8,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0013","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[2,-6,0,2],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, -6, 0, 2], [是, 是, 否, 是], [0, 1, 3])","explanation_zh":"應用基礎核對=([2, -6, 0, 2], [是, 是, 否, 是], [0, 1, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204013,"parameters":{"values":[2,-6,0,2],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[2,-6,0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0014","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[3,-3,-1,3],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, -3, -1, 3], [是, 否, 是, 是], [0, 2, 3])","explanation_zh":"應用基礎核對=([3, -3, -1, 3], [是, 否, 是, 是], [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204014,"parameters":{"values":[3,-3,-1,3],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[3,-3,-1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0015","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[4,0,-2,4],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([4, 0, -2, 4], [是, 是, 是, 是], [0, 1, 2, 3])","explanation_zh":"應用基礎核對=([4, 0, -2, 4], [是, 是, 是, 是], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204015,"parameters":{"values":[4,0,-2,4],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[4,0,-2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0016","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[5,3,-3,0],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([5, 3, -3, 0], [是, 否, 否, 是], [0, 3])","explanation_zh":"應用基礎核對=([5, 3, -3, 0], [是, 否, 否, 是], [0, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204016,"parameters":{"values":[5,3,-3,0],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,false,true],\"values\":[5,3,-3,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0017","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[6,6,-4,1],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([6, 6, -4, 1], [是, 是, 是, 是], [0, 1, 2, 3])","explanation_zh":"應用基礎核對=([6, 6, -4, 1], [是, 是, 是, 是], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204017,"parameters":{"values":[6,6,-4,1],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[6,6,-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0018","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[7,-8,-5,2],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([7, -8, -5, 2], [是, 否, 是, 是], [0, 2, 3])","explanation_zh":"應用基礎核對=([7, -8, -5, 2], [是, 否, 是, 是], [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204018,"parameters":{"values":[7,-8,-5,2],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[7,-8,-5,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0019","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[8,-5,-6,3],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([8, -5, -6, 3], [是, 是, 否, 是], [0, 1, 3])","explanation_zh":"應用基礎核對=([8, -5, -6, 3], [是, 是, 否, 是], [0, 1, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204019,"parameters":{"values":[8,-5,-6,3],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[8,-5,-6,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0020","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[9,-2,-7,4],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([9, -2, -7, 4], [是, 否, 是, 是], [0, 2, 3])","explanation_zh":"應用基礎核對=([9, -2, -7, 4], [是, 否, 是, 是], [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204020,"parameters":{"values":[9,-2,-7,4],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[9,-2,-7,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0021","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[10,1,-8,0],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([10, 1, -8, 0], [是, 是, 是, 是], [0, 1, 2, 3])","explanation_zh":"應用基礎核對=([10, 1, -8, 0], [是, 是, 是, 是], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204021,"parameters":{"values":[10,1,-8,0],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[10,1,-8,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0022","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[11,4,-9,1],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([11, 4, -9, 1], [是, 否, 否, 是], [0, 3])","explanation_zh":"應用基礎核對=([11, 4, -9, 1], [是, 否, 否, 是], [0, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204022,"parameters":{"values":[11,4,-9,1],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,false,true],\"values\":[11,4,-9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0023","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[12,7,-10,2],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([12, 7, -10, 2], [是, 是, 是, 是], [0, 1, 2, 3])","explanation_zh":"應用基礎核對=([12, 7, -10, 2], [是, 是, 是, 是], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204023,"parameters":{"values":[12,7,-10,2],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,true,true],\"values\":[12,7,-10,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0024","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[13,-7,-11,3],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([13, -7, -11, 3], [是, 否, 是, 是], [0, 2, 3])","explanation_zh":"應用基礎核對=([13, -7, -11, 3], [是, 否, 是, 是], [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204024,"parameters":{"values":[13,-7,-11,3],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,false,true,true],\"values\":[13,-7,-11,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0025","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-feasible-filter；資料={\"values\":[14,-4,-12,4],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,feasible_indices] 欄序回答。","answer":{"kind":"expression","value":"([14, -4, -12, 4], [是, 是, 否, 是], [0, 1, 3])","explanation_zh":"應用基礎核對=([14, -4, -12, 4], [是, 是, 否, 是], [0, 1, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-feasible-filter","seed":202610204025,"parameters":{"values":[14,-4,-12,4],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-feasible-filter","semantic_template":"qf-app20-optimization-feasible-filter/{\"feasible\":[true,true,false,true],\"values\":[14,-4,-12,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0026","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-10,-8,12,0],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-10, -8, 12, 0], [是, 是, 否, 是], min, -10, [0])","explanation_zh":"應用基礎核對=([-10, -8, 12, 0], [是, 是, 否, 是], min, -10, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204026,"parameters":{"values":[-10,-8,12,0],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[-10,-8,12,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0027","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-9,-5,11,1],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-9, -5, 11, 1], [是, 否, 是, 是], min, -9, [0])","explanation_zh":"應用基礎核對=([-9, -5, 11, 1], [是, 否, 是, 是], min, -9, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204027,"parameters":{"values":[-9,-5,11,1],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[-9,-5,11,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0028","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-8,-2,10,2],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-8, -2, 10, 2], [是, 是, 是, 是], min, -8, [0])","explanation_zh":"應用基礎核對=([-8, -2, 10, 2], [是, 是, 是, 是], min, -8, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204028,"parameters":{"values":[-8,-2,10,2],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[-8,-2,10,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0029","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-7,1,9,3],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-7, 1, 9, 3], [是, 否, 否, 是], min, -7, [0])","explanation_zh":"應用基礎核對=([-7, 1, 9, 3], [是, 否, 否, 是], min, -7, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204029,"parameters":{"values":[-7,1,9,3],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,false,true],\"values\":[-7,1,9,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0030","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-6,4,8,4],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-6, 4, 8, 4], [是, 是, 是, 是], min, -6, [0])","explanation_zh":"應用基礎核對=([-6, 4, 8, 4], [是, 是, 是, 是], min, -6, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204030,"parameters":{"values":[-6,4,8,4],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[-6,4,8,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0031","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-5,7,7,0],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-5, 7, 7, 0], [是, 否, 是, 是], min, -5, [0])","explanation_zh":"應用基礎核對=([-5, 7, 7, 0], [是, 否, 是, 是], min, -5, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204031,"parameters":{"values":[-5,7,7,0],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[-5,7,7,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0032","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-4,-7,6,1],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-4, -7, 6, 1], [是, 是, 否, 是], min, -7, [1])","explanation_zh":"應用基礎核對=([-4, -7, 6, 1], [是, 是, 否, 是], min, -7, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204032,"parameters":{"values":[-4,-7,6,1],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[-4,-7,6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0033","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-3,-4,5,2],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-3, -4, 5, 2], [是, 否, 是, 是], min, -3, [0])","explanation_zh":"應用基礎核對=([-3, -4, 5, 2], [是, 否, 是, 是], min, -3, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204033,"parameters":{"values":[-3,-4,5,2],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[-3,-4,5,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0034","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-2,-1,4,3],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-2, -1, 4, 3], [是, 是, 是, 是], min, -2, [0])","explanation_zh":"應用基礎核對=([-2, -1, 4, 3], [是, 是, 是, 是], min, -2, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204034,"parameters":{"values":[-2,-1,4,3],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[-2,-1,4,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0035","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[-1,2,3,4],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2, 3, 4], [是, 否, 否, 是], min, -1, [0])","explanation_zh":"應用基礎核對=([-1, 2, 3, 4], [是, 否, 否, 是], min, -1, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204035,"parameters":{"values":[-1,2,3,4],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,false,true],\"values\":[-1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0036","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[0,5,2,0],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([0, 5, 2, 0], [是, 是, 是, 是], min, 0, [0, 3])","explanation_zh":"應用基礎核對=([0, 5, 2, 0], [是, 是, 是, 是], min, 0, [0, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204036,"parameters":{"values":[0,5,2,0],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[0,5,2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0037","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[1,8,1,1],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 8, 1, 1], [是, 否, 是, 是], min, 1, [0, 2, 3])","explanation_zh":"應用基礎核對=([1, 8, 1, 1], [是, 否, 是, 是], min, 1, [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204037,"parameters":{"values":[1,8,1,1],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[1,8,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0038","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[2,-6,0,2],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, -6, 0, 2], [是, 是, 否, 是], min, -6, [1])","explanation_zh":"應用基礎核對=([2, -6, 0, 2], [是, 是, 否, 是], min, -6, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204038,"parameters":{"values":[2,-6,0,2],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[2,-6,0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0039","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[3,-3,-1,3],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, -3, -1, 3], [是, 否, 是, 是], min, -1, [2])","explanation_zh":"應用基礎核對=([3, -3, -1, 3], [是, 否, 是, 是], min, -1, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204039,"parameters":{"values":[3,-3,-1,3],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[3,-3,-1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0040","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[4,0,-2,4],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([4, 0, -2, 4], [是, 是, 是, 是], min, -2, [2])","explanation_zh":"應用基礎核對=([4, 0, -2, 4], [是, 是, 是, 是], min, -2, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204040,"parameters":{"values":[4,0,-2,4],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[4,0,-2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0041","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[5,3,-3,0],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([5, 3, -3, 0], [是, 否, 否, 是], min, 0, [3])","explanation_zh":"應用基礎核對=([5, 3, -3, 0], [是, 否, 否, 是], min, 0, [3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204041,"parameters":{"values":[5,3,-3,0],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,false,true],\"values\":[5,3,-3,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0042","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[6,6,-4,1],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([6, 6, -4, 1], [是, 是, 是, 是], min, -4, [2])","explanation_zh":"應用基礎核對=([6, 6, -4, 1], [是, 是, 是, 是], min, -4, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204042,"parameters":{"values":[6,6,-4,1],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[6,6,-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0043","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[7,-8,-5,2],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([7, -8, -5, 2], [是, 否, 是, 是], min, -5, [2])","explanation_zh":"應用基礎核對=([7, -8, -5, 2], [是, 否, 是, 是], min, -5, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204043,"parameters":{"values":[7,-8,-5,2],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[7,-8,-5,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0044","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[8,-5,-6,3],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([8, -5, -6, 3], [是, 是, 否, 是], min, -5, [1])","explanation_zh":"應用基礎核對=([8, -5, -6, 3], [是, 是, 否, 是], min, -5, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204044,"parameters":{"values":[8,-5,-6,3],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[8,-5,-6,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0045","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[9,-2,-7,4],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([9, -2, -7, 4], [是, 否, 是, 是], min, -7, [2])","explanation_zh":"應用基礎核對=([9, -2, -7, 4], [是, 否, 是, 是], min, -7, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204045,"parameters":{"values":[9,-2,-7,4],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[9,-2,-7,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0046","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[10,1,-8,0],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([10, 1, -8, 0], [是, 是, 是, 是], min, -8, [2])","explanation_zh":"應用基礎核對=([10, 1, -8, 0], [是, 是, 是, 是], min, -8, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204046,"parameters":{"values":[10,1,-8,0],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[10,1,-8,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0047","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[11,4,-9,1],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([11, 4, -9, 1], [是, 否, 否, 是], min, 1, [3])","explanation_zh":"應用基礎核對=([11, 4, -9, 1], [是, 否, 否, 是], min, 1, [3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204047,"parameters":{"values":[11,4,-9,1],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,false,true],\"values\":[11,4,-9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0048","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[12,7,-10,2],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([12, 7, -10, 2], [是, 是, 是, 是], min, -10, [2])","explanation_zh":"應用基礎核對=([12, 7, -10, 2], [是, 是, 是, 是], min, -10, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204048,"parameters":{"values":[12,7,-10,2],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,true,true],\"values\":[12,7,-10,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0049","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[13,-7,-11,3],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([13, -7, -11, 3], [是, 否, 是, 是], min, -11, [2])","explanation_zh":"應用基礎核對=([13, -7, -11, 3], [是, 否, 是, 是], min, -11, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204049,"parameters":{"values":[13,-7,-11,3],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,false,true,true],\"values\":[13,-7,-11,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0050","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmin；資料={\"values\":[14,-4,-12,4],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,min,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([14, -4, -12, 4], [是, 是, 否, 是], min, -4, [1])","explanation_zh":"應用基礎核對=([14, -4, -12, 4], [是, 是, 否, 是], min, -4, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmin","seed":202610204050,"parameters":{"values":[14,-4,-12,4],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmin","semantic_template":"qf-app20-optimization-argmin/{\"feasible\":[true,true,false,true],\"values\":[14,-4,-12,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0051","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-10,-8,12,0],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-10, -8, 12, 0], [是, 是, 否, 是], max, 0, [3])","explanation_zh":"應用基礎核對=([-10, -8, 12, 0], [是, 是, 否, 是], max, 0, [3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204051,"parameters":{"values":[-10,-8,12,0],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[-10,-8,12,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0052","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-9,-5,11,1],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-9, -5, 11, 1], [是, 否, 是, 是], max, 11, [2])","explanation_zh":"應用基礎核對=([-9, -5, 11, 1], [是, 否, 是, 是], max, 11, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204052,"parameters":{"values":[-9,-5,11,1],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[-9,-5,11,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0053","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-8,-2,10,2],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-8, -2, 10, 2], [是, 是, 是, 是], max, 10, [2])","explanation_zh":"應用基礎核對=([-8, -2, 10, 2], [是, 是, 是, 是], max, 10, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204053,"parameters":{"values":[-8,-2,10,2],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[-8,-2,10,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0054","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-7,1,9,3],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-7, 1, 9, 3], [是, 否, 否, 是], max, 3, [3])","explanation_zh":"應用基礎核對=([-7, 1, 9, 3], [是, 否, 否, 是], max, 3, [3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204054,"parameters":{"values":[-7,1,9,3],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,false,true],\"values\":[-7,1,9,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0055","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-6,4,8,4],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-6, 4, 8, 4], [是, 是, 是, 是], max, 8, [2])","explanation_zh":"應用基礎核對=([-6, 4, 8, 4], [是, 是, 是, 是], max, 8, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204055,"parameters":{"values":[-6,4,8,4],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[-6,4,8,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0056","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-5,7,7,0],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-5, 7, 7, 0], [是, 否, 是, 是], max, 7, [2])","explanation_zh":"應用基礎核對=([-5, 7, 7, 0], [是, 否, 是, 是], max, 7, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204056,"parameters":{"values":[-5,7,7,0],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[-5,7,7,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0057","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-4,-7,6,1],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-4, -7, 6, 1], [是, 是, 否, 是], max, 1, [3])","explanation_zh":"應用基礎核對=([-4, -7, 6, 1], [是, 是, 否, 是], max, 1, [3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204057,"parameters":{"values":[-4,-7,6,1],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[-4,-7,6,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0058","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-3,-4,5,2],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-3, -4, 5, 2], [是, 否, 是, 是], max, 5, [2])","explanation_zh":"應用基礎核對=([-3, -4, 5, 2], [是, 否, 是, 是], max, 5, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204058,"parameters":{"values":[-3,-4,5,2],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[-3,-4,5,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0059","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-2,-1,4,3],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-2, -1, 4, 3], [是, 是, 是, 是], max, 4, [2])","explanation_zh":"應用基礎核對=([-2, -1, 4, 3], [是, 是, 是, 是], max, 4, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204059,"parameters":{"values":[-2,-1,4,3],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[-2,-1,4,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0060","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[-1,2,3,4],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2, 3, 4], [是, 否, 否, 是], max, 4, [3])","explanation_zh":"應用基礎核對=([-1, 2, 3, 4], [是, 否, 否, 是], max, 4, [3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204060,"parameters":{"values":[-1,2,3,4],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,false,true],\"values\":[-1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0061","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[0,5,2,0],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([0, 5, 2, 0], [是, 是, 是, 是], max, 5, [1])","explanation_zh":"應用基礎核對=([0, 5, 2, 0], [是, 是, 是, 是], max, 5, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204061,"parameters":{"values":[0,5,2,0],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[0,5,2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0062","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[1,8,1,1],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 8, 1, 1], [是, 否, 是, 是], max, 1, [0, 2, 3])","explanation_zh":"應用基礎核對=([1, 8, 1, 1], [是, 否, 是, 是], max, 1, [0, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204062,"parameters":{"values":[1,8,1,1],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[1,8,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0063","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[2,-6,0,2],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, -6, 0, 2], [是, 是, 否, 是], max, 2, [0, 3])","explanation_zh":"應用基礎核對=([2, -6, 0, 2], [是, 是, 否, 是], max, 2, [0, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204063,"parameters":{"values":[2,-6,0,2],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[2,-6,0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0064","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[3,-3,-1,3],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, -3, -1, 3], [是, 否, 是, 是], max, 3, [0, 3])","explanation_zh":"應用基礎核對=([3, -3, -1, 3], [是, 否, 是, 是], max, 3, [0, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204064,"parameters":{"values":[3,-3,-1,3],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[3,-3,-1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0065","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[4,0,-2,4],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([4, 0, -2, 4], [是, 是, 是, 是], max, 4, [0, 3])","explanation_zh":"應用基礎核對=([4, 0, -2, 4], [是, 是, 是, 是], max, 4, [0, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204065,"parameters":{"values":[4,0,-2,4],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[4,0,-2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0066","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[5,3,-3,0],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([5, 3, -3, 0], [是, 否, 否, 是], max, 5, [0])","explanation_zh":"應用基礎核對=([5, 3, -3, 0], [是, 否, 否, 是], max, 5, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204066,"parameters":{"values":[5,3,-3,0],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,false,true],\"values\":[5,3,-3,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0067","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[6,6,-4,1],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([6, 6, -4, 1], [是, 是, 是, 是], max, 6, [0, 1])","explanation_zh":"應用基礎核對=([6, 6, -4, 1], [是, 是, 是, 是], max, 6, [0, 1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204067,"parameters":{"values":[6,6,-4,1],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[6,6,-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0068","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[7,-8,-5,2],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([7, -8, -5, 2], [是, 否, 是, 是], max, 7, [0])","explanation_zh":"應用基礎核對=([7, -8, -5, 2], [是, 否, 是, 是], max, 7, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204068,"parameters":{"values":[7,-8,-5,2],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[7,-8,-5,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0069","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[8,-5,-6,3],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([8, -5, -6, 3], [是, 是, 否, 是], max, 8, [0])","explanation_zh":"應用基礎核對=([8, -5, -6, 3], [是, 是, 否, 是], max, 8, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204069,"parameters":{"values":[8,-5,-6,3],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[8,-5,-6,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0070","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[9,-2,-7,4],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([9, -2, -7, 4], [是, 否, 是, 是], max, 9, [0])","explanation_zh":"應用基礎核對=([9, -2, -7, 4], [是, 否, 是, 是], max, 9, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204070,"parameters":{"values":[9,-2,-7,4],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[9,-2,-7,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0071","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[10,1,-8,0],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([10, 1, -8, 0], [是, 是, 是, 是], max, 10, [0])","explanation_zh":"應用基礎核對=([10, 1, -8, 0], [是, 是, 是, 是], max, 10, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204071,"parameters":{"values":[10,1,-8,0],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[10,1,-8,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0072","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[11,4,-9,1],\"feasible\":[true,false,false,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([11, 4, -9, 1], [是, 否, 否, 是], max, 11, [0])","explanation_zh":"應用基礎核對=([11, 4, -9, 1], [是, 否, 否, 是], max, 11, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204072,"parameters":{"values":[11,4,-9,1],"feasible":[true,false,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,false,true],\"values\":[11,4,-9,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0073","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[12,7,-10,2],\"feasible\":[true,true,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([12, 7, -10, 2], [是, 是, 是, 是], max, 12, [0])","explanation_zh":"應用基礎核對=([12, 7, -10, 2], [是, 是, 是, 是], max, 12, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204073,"parameters":{"values":[12,7,-10,2],"feasible":[true,true,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,true,true],\"values\":[12,7,-10,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0074","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[13,-7,-11,3],\"feasible\":[true,false,true,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([13, -7, -11, 3], [是, 否, 是, 是], max, 13, [0])","explanation_zh":"應用基礎核對=([13, -7, -11, 3], [是, 否, 是, 是], max, 13, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204074,"parameters":{"values":[13,-7,-11,3],"feasible":[true,false,true,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,false,true,true],\"values\":[13,-7,-11,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0075","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-argmax；資料={\"values\":[14,-4,-12,4],\"feasible\":[true,true,false,true]}。請依 [values,feasible_mask,max,value,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([14, -4, -12, 4], [是, 是, 否, 是], max, 14, [0])","explanation_zh":"應用基礎核對=([14, -4, -12, 4], [是, 是, 否, 是], max, 14, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-argmax","seed":202610204075,"parameters":{"values":[14,-4,-12,4],"feasible":[true,true,false,true],"domain":"Finite_declared_optimization","operation":"optimization-argmax","semantic_template":"qf-app20-optimization-argmax/{\"feasible\":[true,true,false,true],\"values\":[14,-4,-12,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0076","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,0],[2,0],[3,0]],\"constraint\":[1,1,5],\"objective\":[-2,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 5], [-2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 0, 是, -4], [3, 3, 0, 是, -6]], 0, [0])","explanation_zh":"應用基礎核對=([1, 1, 5], [-2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 0, 是, -4], [3, 3, 0, 是, -6]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204076,"parameters":{"points":[[0,0],[1,0],[2,0],[3,0]],"constraint":[1,1,5],"objective":[-2,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,5],\"direction\":\"max\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,0],[3,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0077","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,1],[2,2],[3,1]],\"constraint\":[2,1,6],\"objective\":[-1,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 6], [-1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 2, 是, 2], [3, 3, 1, 否, -1]], 0, [0])","explanation_zh":"應用基礎核對=([2, 1, 6], [-1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 2, 是, 2], [3, 3, 1, 否, -1]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204077,"parameters":{"points":[[0,0],[1,1],[2,2],[3,1]],"constraint":[2,1,6],"objective":[-1,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,6],\"direction\":\"min\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,2],[3,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0078","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,2],[2,4],[3,2]],\"constraint\":[3,1,7],\"objective\":[0,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 7], [0, 2], max, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 4, 否, 8], [3, 3, 2, 否, 4]], 4, [1])","explanation_zh":"應用基礎核對=([3, 1, 7], [0, 2], max, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 4, 否, 8], [3, 3, 2, 否, 4]], 4, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204078,"parameters":{"points":[[0,0],[1,2],[2,4],[3,2]],"constraint":[3,1,7],"objective":[0,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,7],\"direction\":\"max\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,4],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0079","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,3],[2,6],[3,3]],\"constraint\":[1,1,8],\"objective\":[1,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 8], [1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 6, 是, 14], [3, 3, 3, 是, 9]], 0, [0])","explanation_zh":"應用基礎核對=([1, 1, 8], [1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 6, 是, 14], [3, 3, 3, 是, 9]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204079,"parameters":{"points":[[0,0],[1,3],[2,6],[3,3]],"constraint":[1,1,8],"objective":[1,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,8],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,6],[3,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0080","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,4],[2,1],[3,0]],\"constraint\":[2,1,9],\"objective\":[2,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 9], [2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 1, 是, 6], [3, 3, 0, 是, 6]], 10, [1])","explanation_zh":"應用基礎核對=([2, 1, 9], [2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 1, 是, 6], [3, 3, 0, 是, 6]], 10, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204080,"parameters":{"points":[[0,0],[1,4],[2,1],[3,0]],"constraint":[2,1,9],"objective":[2,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,9],\"direction\":\"max\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,1],[3,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0081","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,0],[2,3],[3,1]],\"constraint\":[3,1,10],\"objective\":[-2,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 10], [-2, 2], min, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 3, 是, 2], [3, 3, 1, 是, -4]], -4, [3])","explanation_zh":"應用基礎核對=([3, 1, 10], [-2, 2], min, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 3, 是, 2], [3, 3, 1, 是, -4]], -4, [3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204081,"parameters":{"points":[[0,0],[1,0],[2,3],[3,1]],"constraint":[3,1,10],"objective":[-2,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,10],\"direction\":\"min\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,3],[3,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0082","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,1],[2,5],[3,2]],\"constraint\":[1,1,11],\"objective\":[-1,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 11], [-1, 2], max, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 5, 是, 8], [3, 3, 2, 是, 1]], 8, [2])","explanation_zh":"應用基礎核對=([1, 1, 11], [-1, 2], max, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 5, 是, 8], [3, 3, 2, 是, 1]], 8, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204082,"parameters":{"points":[[0,0],[1,1],[2,5],[3,2]],"constraint":[1,1,11],"objective":[-1,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,11],\"direction\":\"max\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,5],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0083","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,2],[2,0],[3,3]],\"constraint\":[2,1,12],\"objective\":[0,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 12], [0, 2], min, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 0, 是, 0], [3, 3, 3, 是, 6]], 0, [0, 2])","explanation_zh":"應用基礎核對=([2, 1, 12], [0, 2], min, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 0, 是, 0], [3, 3, 3, 是, 6]], 0, [0, 2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204083,"parameters":{"points":[[0,0],[1,2],[2,0],[3,3]],"constraint":[2,1,12],"objective":[0,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,12],\"direction\":\"min\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,0],[3,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0084","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,3],[2,2],[3,0]],\"constraint\":[3,1,5],\"objective\":[1,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 5], [1, 2], max, [[0, 0, 0, 是, 0], [1, 1, 3, 否, 7], [2, 2, 2, 否, 6], [3, 3, 0, 否, 3]], 0, [0])","explanation_zh":"應用基礎核對=([3, 1, 5], [1, 2], max, [[0, 0, 0, 是, 0], [1, 1, 3, 否, 7], [2, 2, 2, 否, 6], [3, 3, 0, 否, 3]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204084,"parameters":{"points":[[0,0],[1,3],[2,2],[3,0]],"constraint":[3,1,5],"objective":[1,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,5],\"direction\":\"max\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,2],[3,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0085","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,4],[2,4],[3,1]],\"constraint\":[1,1,6],\"objective\":[2,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 6], [2, 2], min, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 4, 是, 12], [3, 3, 1, 是, 8]], 0, [0])","explanation_zh":"應用基礎核對=([1, 1, 6], [2, 2], min, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 4, 是, 12], [3, 3, 1, 是, 8]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204085,"parameters":{"points":[[0,0],[1,4],[2,4],[3,1]],"constraint":[1,1,6],"objective":[2,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,6],\"direction\":\"min\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,4],[3,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0086","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,0],[2,6],[3,2]],\"constraint\":[2,1,7],\"objective\":[-2,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 7], [-2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 6, 否, 8], [3, 3, 2, 否, -2]], 0, [0])","explanation_zh":"應用基礎核對=([2, 1, 7], [-2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 6, 否, 8], [3, 3, 2, 否, -2]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204086,"parameters":{"points":[[0,0],[1,0],[2,6],[3,2]],"constraint":[2,1,7],"objective":[-2,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,7],\"direction\":\"max\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,6],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0087","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,1],[2,1],[3,3]],\"constraint\":[3,1,8],\"objective\":[-1,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 8], [-1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 1, 是, 0], [3, 3, 3, 否, 3]], 0, [0, 2])","explanation_zh":"應用基礎核對=([3, 1, 8], [-1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 1, 是, 0], [3, 3, 3, 否, 3]], 0, [0, 2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204087,"parameters":{"points":[[0,0],[1,1],[2,1],[3,3]],"constraint":[3,1,8],"objective":[-1,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,8],\"direction\":\"min\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,1],[3,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0088","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,2],[2,3],[3,0]],\"constraint\":[1,1,9],\"objective\":[0,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 9], [0, 2], max, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 3, 是, 6], [3, 3, 0, 是, 0]], 6, [2])","explanation_zh":"應用基礎核對=([1, 1, 9], [0, 2], max, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 3, 是, 6], [3, 3, 0, 是, 0]], 6, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204088,"parameters":{"points":[[0,0],[1,2],[2,3],[3,0]],"constraint":[1,1,9],"objective":[0,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,9],\"direction\":\"max\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,3],[3,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0089","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,3],[2,5],[3,1]],\"constraint\":[2,1,10],\"objective\":[1,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 10], [1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 5, 是, 12], [3, 3, 1, 是, 5]], 0, [0])","explanation_zh":"應用基礎核對=([2, 1, 10], [1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 5, 是, 12], [3, 3, 1, 是, 5]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204089,"parameters":{"points":[[0,0],[1,3],[2,5],[3,1]],"constraint":[2,1,10],"objective":[1,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,10],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,5],[3,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0090","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,4],[2,0],[3,2]],\"constraint\":[3,1,11],\"objective\":[2,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 11], [2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 0, 是, 4], [3, 3, 2, 是, 10]], 10, [1, 3])","explanation_zh":"應用基礎核對=([3, 1, 11], [2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 0, 是, 4], [3, 3, 2, 是, 10]], 10, [1, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204090,"parameters":{"points":[[0,0],[1,4],[2,0],[3,2]],"constraint":[3,1,11],"objective":[2,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,11],\"direction\":\"max\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,0],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0091","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,0],[2,2],[3,3]],\"constraint\":[1,1,12],\"objective\":[-2,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 12], [-2, 2], min, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 2, 是, 0], [3, 3, 3, 是, 0]], -2, [1])","explanation_zh":"應用基礎核對=([1, 1, 12], [-2, 2], min, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 2, 是, 0], [3, 3, 3, 是, 0]], -2, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204091,"parameters":{"points":[[0,0],[1,0],[2,2],[3,3]],"constraint":[1,1,12],"objective":[-2,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,12],\"direction\":\"min\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,2],[3,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0092","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,1],[2,4],[3,0]],\"constraint\":[2,1,5],\"objective\":[-1,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 5], [-1, 2], max, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 4, 否, 6], [3, 3, 0, 否, -3]], 1, [1])","explanation_zh":"應用基礎核對=([2, 1, 5], [-1, 2], max, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 4, 否, 6], [3, 3, 0, 否, -3]], 1, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204092,"parameters":{"points":[[0,0],[1,1],[2,4],[3,0]],"constraint":[2,1,5],"objective":[-1,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,5],\"direction\":\"max\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,4],[3,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0093","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,2],[2,6],[3,1]],\"constraint\":[3,1,6],\"objective\":[0,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 6], [0, 2], min, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 6, 否, 12], [3, 3, 1, 否, 2]], 0, [0])","explanation_zh":"應用基礎核對=([3, 1, 6], [0, 2], min, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 6, 否, 12], [3, 3, 1, 否, 2]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204093,"parameters":{"points":[[0,0],[1,2],[2,6],[3,1]],"constraint":[3,1,6],"objective":[0,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,6],\"direction\":\"min\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,6],[3,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0094","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,3],[2,1],[3,2]],\"constraint\":[1,1,7],\"objective\":[1,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 7], [1, 2], max, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 1, 是, 4], [3, 3, 2, 是, 7]], 7, [1, 3])","explanation_zh":"應用基礎核對=([1, 1, 7], [1, 2], max, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 1, 是, 4], [3, 3, 2, 是, 7]], 7, [1, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204094,"parameters":{"points":[[0,0],[1,3],[2,1],[3,2]],"constraint":[1,1,7],"objective":[1,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,7],\"direction\":\"max\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,1],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0095","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,4],[2,3],[3,3]],\"constraint\":[2,1,8],\"objective\":[2,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 8], [2, 2], min, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 3, 是, 10], [3, 3, 3, 否, 12]], 0, [0])","explanation_zh":"應用基礎核對=([2, 1, 8], [2, 2], min, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 3, 是, 10], [3, 3, 3, 否, 12]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204095,"parameters":{"points":[[0,0],[1,4],[2,3],[3,3]],"constraint":[2,1,8],"objective":[2,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,8],\"direction\":\"min\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,3],[3,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0096","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,0],[2,5],[3,0]],\"constraint\":[3,1,9],\"objective\":[-2,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 9], [-2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 5, 否, 6], [3, 3, 0, 是, -6]], 0, [0])","explanation_zh":"應用基礎核對=([3, 1, 9], [-2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 0, 是, -2], [2, 2, 5, 否, 6], [3, 3, 0, 是, -6]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204096,"parameters":{"points":[[0,0],[1,0],[2,5],[3,0]],"constraint":[3,1,9],"objective":[-2,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,9],\"direction\":\"max\",\"objective\":[-2,2],\"points\":[[0,0],[1,0],[2,5],[3,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0097","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,1],[2,0],[3,1]],\"constraint\":[1,1,10],\"objective\":[-1,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 10], [-1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 0, 是, -2], [3, 3, 1, 是, -1]], -2, [2])","explanation_zh":"應用基礎核對=([1, 1, 10], [-1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 1, 是, 1], [2, 2, 0, 是, -2], [3, 3, 1, 是, -1]], -2, [2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204097,"parameters":{"points":[[0,0],[1,1],[2,0],[3,1]],"constraint":[1,1,10],"objective":[-1,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,10],\"direction\":\"min\",\"objective\":[-1,2],\"points\":[[0,0],[1,1],[2,0],[3,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0098","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,2],[2,2],[3,2]],\"constraint\":[2,1,11],\"objective\":[0,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 11], [0, 2], max, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 2, 是, 4], [3, 3, 2, 是, 4]], 4, [1, 2, 3])","explanation_zh":"應用基礎核對=([2, 1, 11], [0, 2], max, [[0, 0, 0, 是, 0], [1, 1, 2, 是, 4], [2, 2, 2, 是, 4], [3, 3, 2, 是, 4]], 4, [1, 2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204098,"parameters":{"points":[[0,0],[1,2],[2,2],[3,2]],"constraint":[2,1,11],"objective":[0,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[2,1,11],\"direction\":\"max\",\"objective\":[0,2],\"points\":[[0,0],[1,2],[2,2],[3,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0099","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,3],[2,4],[3,3]],\"constraint\":[3,1,12],\"objective\":[1,2],\"direction\":\"min\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 12], [1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 4, 是, 10], [3, 3, 3, 是, 9]], 0, [0])","explanation_zh":"應用基礎核對=([3, 1, 12], [1, 2], min, [[0, 0, 0, 是, 0], [1, 1, 3, 是, 7], [2, 2, 4, 是, 10], [3, 3, 3, 是, 9]], 0, [0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204099,"parameters":{"points":[[0,0],[1,3],[2,4],[3,3]],"constraint":[3,1,12],"objective":[1,2],"direction":"min","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[3,1,12],\"direction\":\"min\",\"objective\":[1,2],\"points\":[[0,0],[1,3],[2,4],[3,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r04-optimization-problem-0100","batch_id":"batch-20261013-advance-20261020-r04-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-optimization-problem"],"title_zh":"有限候選最佳化","stem_zh":"完整明示有限可行候選。操作=optimization-linear-constraint-audit；資料={\"points\":[[0,0],[1,4],[2,6],[3,0]],\"constraint\":[1,1,5],\"objective\":[2,2],\"direction\":\"max\"}。請依 [constraint,objective,direction,rows,best,arg_indices] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 5], [2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 6, 否, 16], [3, 3, 0, 是, 6]], 10, [1])","explanation_zh":"應用基礎核對=([1, 1, 5], [2, 2], max, [[0, 0, 0, 是, 0], [1, 1, 4, 是, 10], [2, 2, 6, 否, 16], [3, 3, 0, 是, 6]], 10, [1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；只證宣告候選集內最優；不宣稱一般最佳化複雜度。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限候選最佳化"]},"variant":{"family_id":"qf-app20-optimization-linear-constraint-audit","seed":202610204100,"parameters":{"points":[[0,0],[1,4],[2,6],[3,0]],"constraint":[1,1,5],"objective":[2,2],"direction":"max","domain":"Finite_declared_optimization","operation":"optimization-linear-constraint-audit","semantic_template":"qf-app20-optimization-linear-constraint-audit/{\"constraint\":[1,1,5],\"direction\":\"max\",\"objective\":[2,2],\"points\":[[0,0],[1,4],[2,6],[3,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}