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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261025-r03-convex-optimization-problem-0002","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[1,-11,-2],\"interval\":[-3,4]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, -11, -2], [-3, 4], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([1, -11, -2], [-3, 4], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253002,"parameters":{"coefficients":[1,-11,-2],"interval":[-3,4],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[1,-11,-2],\"interval\":[-3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0003","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[2,-10,-1],\"interval\":[-4,5]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, -10, -1], [-4, 5], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([2, -10, -1], [-4, 5], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253003,"parameters":{"coefficients":[2,-10,-1],"interval":[-4,5],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[2,-10,-1],\"interval\":[-4,5]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0004","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[3,-9,0],\"interval\":[-5,6]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, -9, 0], [-5, 6], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([3, -9, 0], [-5, 6], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253004,"parameters":{"coefficients":[3,-9,0],"interval":[-5,6],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[3,-9,0],\"interval\":[-5,6]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0005","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[0,-8,1],\"interval\":[-6,7]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, -8, 1], [-6, 7], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([0, -8, 1], [-6, 7], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253005,"parameters":{"coefficients":[0,-8,1],"interval":[-6,7],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[0,-8,1],\"interval\":[-6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0006","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[-1,-7,2],\"interval\":[-7,8]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([-1, -7, 2], [-7, 8], 否, 是, 否, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([-1, -7, 2], [-7, 8], 否, 是, 否, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253006,"parameters":{"coefficients":[-1,-7,2],"interval":[-7,8],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[-1,-7,2],\"interval\":[-7,8]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0007","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[2,-6,3],\"interval\":[-8,9]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, -6, 3], [-8, 9], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([2, -6, 3], [-8, 9], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253007,"parameters":{"coefficients":[2,-6,3],"interval":[-8,9],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[2,-6,3],\"interval\":[-8,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0008","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[3,-5,-3],\"interval\":[-9,10]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, -5, -3], [-9, 10], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([3, -5, -3], [-9, 10], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253008,"parameters":{"coefficients":[3,-5,-3],"interval":[-9,10],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[3,-5,-3],\"interval\":[-9,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0009","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[0,-4,-2],\"interval\":[-10,11]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, -4, -2], [-10, 11], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([0, -4, -2], [-10, 11], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253009,"parameters":{"coefficients":[0,-4,-2],"interval":[-10,11],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[0,-4,-2],\"interval\":[-10,11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0010","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[1,-3,-1],\"interval\":[-11,12]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, -3, -1], [-11, 12], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([1, -3, -1], [-11, 12], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253010,"parameters":{"coefficients":[1,-3,-1],"interval":[-11,12],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[1,-3,-1],\"interval\":[-11,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0011","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[-1,-2,0],\"interval\":[-12,13]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([-1, -2, 0], [-12, 13], 否, 是, 否, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([-1, -2, 0], [-12, 13], 否, 是, 否, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253011,"parameters":{"coefficients":[-1,-2,0],"interval":[-12,13],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[-1,-2,0],\"interval\":[-12,13]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0012","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[3,-1,1],\"interval\":[-13,14]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, -1, 1], [-13, 14], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([3, -1, 1], [-13, 14], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253012,"parameters":{"coefficients":[3,-1,1],"interval":[-13,14],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[3,-1,1],\"interval\":[-13,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0013","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[0,0,2],\"interval\":[-14,15]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 2], [-14, 15], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([0, 0, 2], [-14, 15], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253013,"parameters":{"coefficients":[0,0,2],"interval":[-14,15],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[0,0,2],\"interval\":[-14,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0014","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[1,1,3],\"interval\":[-15,16]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 3], [-15, 16], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([1, 1, 3], [-15, 16], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253014,"parameters":{"coefficients":[1,1,3],"interval":[-15,16],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[1,1,3],\"interval\":[-15,16]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0015","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[2,2,-3],\"interval\":[-16,17]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, 2, -3], [-16, 17], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([2, 2, -3], [-16, 17], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253015,"parameters":{"coefficients":[2,2,-3],"interval":[-16,17],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[2,2,-3],\"interval\":[-16,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0016","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[-1,3,-2],\"interval\":[-17,18]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([-1, 3, -2], [-17, 18], 否, 是, 否, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([-1, 3, -2], [-17, 18], 否, 是, 否, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253016,"parameters":{"coefficients":[-1,3,-2],"interval":[-17,18],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[-1,3,-2],\"interval\":[-17,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0017","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[0,4,-1],\"interval\":[-18,19]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 4, -1], [-18, 19], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([0, 4, -1], [-18, 19], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253017,"parameters":{"coefficients":[0,4,-1],"interval":[-18,19],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[0,4,-1],\"interval\":[-18,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0018","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[1,5,0],\"interval\":[-19,20]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, 5, 0], [-19, 20], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([1, 5, 0], [-19, 20], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253018,"parameters":{"coefficients":[1,5,0],"interval":[-19,20],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[1,5,0],\"interval\":[-19,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0019","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[2,6,1],\"interval\":[-20,21]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, 6, 1], [-20, 21], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([2, 6, 1], [-20, 21], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253019,"parameters":{"coefficients":[2,6,1],"interval":[-20,21],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[2,6,1],\"interval\":[-20,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0020","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[3,7,2],\"interval\":[-21,22]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, 7, 2], [-21, 22], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([3, 7, 2], [-21, 22], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253020,"parameters":{"coefficients":[3,7,2],"interval":[-21,22],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[3,7,2],\"interval\":[-21,22]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0021","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[-1,8,3],\"interval\":[-22,23]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([-1, 8, 3], [-22, 23], 否, 是, 否, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([-1, 8, 3], [-22, 23], 否, 是, 否, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253021,"parameters":{"coefficients":[-1,8,3],"interval":[-22,23],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[-1,8,3],\"interval\":[-22,23]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0022","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[1,9,-3],\"interval\":[-23,24]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, 9, -3], [-23, 24], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([1, 9, -3], [-23, 24], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253022,"parameters":{"coefficients":[1,9,-3],"interval":[-23,24],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[1,9,-3],\"interval\":[-23,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0023","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[2,10,-2],\"interval\":[-24,25]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, 10, -2], [-24, 25], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([2, 10, -2], [-24, 25], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253023,"parameters":{"coefficients":[2,10,-2],"interval":[-24,25],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[2,10,-2],\"interval\":[-24,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0024","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[3,11,-1],\"interval\":[-25,26]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, 11, -1], [-25, 26], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([3, 11, -1], [-25, 26], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253024,"parameters":{"coefficients":[3,11,-1],"interval":[-25,26],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[3,11,-1],\"interval\":[-25,26]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0025","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-problem-qualification；資料={\"coefficients\":[0,12,0],\"interval\":[-26,27]}。請依 [coefficients,interval,objective_convex,feasible_set_convex,qualified,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 12, 0], [-26, 27], 是, 是, 是, qualification_only_no_solution_claim)","explanation_zh":"收束波核對=([0, 12, 0], [-26, 27], 是, 是, 是, qualification_only_no_solution_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-problem-qualification","seed":202610253025,"parameters":{"coefficients":[0,12,0],"interval":[-26,27],"domain":"Exact_interval_convex_optimization","operation":"convexopt-problem-qualification","semantic_template":"qf-mod25-convexopt-problem-qualification/{\"coefficients\":[0,12,0],\"interval\":[-26,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0026","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-2,3],\"point\":[-3,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-2, 3], -3, 否, feasibility_only)","explanation_zh":"收束波核對=([-2, 3], -3, 否, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253026,"parameters":{"interval":[-2,3],"point":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-2,3],\"point\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0027","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-3,4],\"point\":[-2,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-3, 4], -2, 是, feasibility_only)","explanation_zh":"收束波核對=([-3, 4], -2, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253027,"parameters":{"interval":[-3,4],"point":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-3,4],\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0028","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-4,5],\"point\":[-1,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-4, 5], -1, 是, feasibility_only)","explanation_zh":"收束波核對=([-4, 5], -1, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253028,"parameters":{"interval":[-4,5],"point":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-4,5],\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0029","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-5,6],\"point\":[0,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-5, 6], 0, 是, feasibility_only)","explanation_zh":"收束波核對=([-5, 6], 0, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253029,"parameters":{"interval":[-5,6],"point":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-5,6],\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0030","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-6,7],\"point\":[1,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-6, 7], 1, 是, feasibility_only)","explanation_zh":"收束波核對=([-6, 7], 1, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253030,"parameters":{"interval":[-6,7],"point":[1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-6,7],\"point\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0031","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-7,8],\"point\":[2,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-7, 8], 2, 是, feasibility_only)","explanation_zh":"收束波核對=([-7, 8], 2, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253031,"parameters":{"interval":[-7,8],"point":[2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-7,8],\"point\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0032","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-8,9],\"point\":[3,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-8, 9], 3, 是, feasibility_only)","explanation_zh":"收束波核對=([-8, 9], 3, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253032,"parameters":{"interval":[-8,9],"point":[3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-8,9],\"point\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0033","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-9,10],\"point\":[-3,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-9, 10], -3, 是, feasibility_only)","explanation_zh":"收束波核對=([-9, 10], -3, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253033,"parameters":{"interval":[-9,10],"point":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-9,10],\"point\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0034","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-10,11],\"point\":[-2,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-10, 11], -2, 是, feasibility_only)","explanation_zh":"收束波核對=([-10, 11], -2, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253034,"parameters":{"interval":[-10,11],"point":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-10,11],\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0035","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-11,12],\"point\":[-1,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-11, 12], -1, 是, feasibility_only)","explanation_zh":"收束波核對=([-11, 12], -1, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253035,"parameters":{"interval":[-11,12],"point":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-11,12],\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0036","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-12,13],\"point\":[0,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-12, 13], 0, 是, feasibility_only)","explanation_zh":"收束波核對=([-12, 13], 0, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253036,"parameters":{"interval":[-12,13],"point":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-12,13],\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0037","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-13,14],\"point\":[1,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-13, 14], 1, 是, feasibility_only)","explanation_zh":"收束波核對=([-13, 14], 1, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253037,"parameters":{"interval":[-13,14],"point":[1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-13,14],\"point\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0038","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-14,15],\"point\":[2,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-14, 15], 2, 是, feasibility_only)","explanation_zh":"收束波核對=([-14, 15], 2, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253038,"parameters":{"interval":[-14,15],"point":[2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-14,15],\"point\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0039","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-15,16],\"point\":[3,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-15, 16], 3, 是, feasibility_only)","explanation_zh":"收束波核對=([-15, 16], 3, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253039,"parameters":{"interval":[-15,16],"point":[3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-15,16],\"point\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0040","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-16,17],\"point\":[-3,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-16, 17], -3, 是, feasibility_only)","explanation_zh":"收束波核對=([-16, 17], -3, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253040,"parameters":{"interval":[-16,17],"point":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-16,17],\"point\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0041","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-17,18],\"point\":[-2,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-17, 18], -2, 是, feasibility_only)","explanation_zh":"收束波核對=([-17, 18], -2, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253041,"parameters":{"interval":[-17,18],"point":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-17,18],\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0042","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-18,19],\"point\":[-1,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-18, 19], -1, 是, feasibility_only)","explanation_zh":"收束波核對=([-18, 19], -1, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253042,"parameters":{"interval":[-18,19],"point":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-18,19],\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0043","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-19,20],\"point\":[0,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-19, 20], 0, 是, feasibility_only)","explanation_zh":"收束波核對=([-19, 20], 0, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253043,"parameters":{"interval":[-19,20],"point":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-19,20],\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0044","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-20,21],\"point\":[1,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-20, 21], 1, 是, feasibility_only)","explanation_zh":"收束波核對=([-20, 21], 1, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253044,"parameters":{"interval":[-20,21],"point":[1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-20,21],\"point\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0045","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-21,22],\"point\":[2,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-21, 22], 2, 是, feasibility_only)","explanation_zh":"收束波核對=([-21, 22], 2, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253045,"parameters":{"interval":[-21,22],"point":[2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-21,22],\"point\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0046","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-22,23],\"point\":[3,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-22, 23], 3, 是, feasibility_only)","explanation_zh":"收束波核對=([-22, 23], 3, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253046,"parameters":{"interval":[-22,23],"point":[3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-22,23],\"point\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0047","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-23,24],\"point\":[-3,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-23, 24], -3, 是, feasibility_only)","explanation_zh":"收束波核對=([-23, 24], -3, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253047,"parameters":{"interval":[-23,24],"point":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-23,24],\"point\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0048","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-24,25],\"point\":[-2,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-24, 25], -2, 是, feasibility_only)","explanation_zh":"收束波核對=([-24, 25], -2, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253048,"parameters":{"interval":[-24,25],"point":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-24,25],\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0049","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-25,26],\"point\":[-1,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-25, 26], -1, 是, feasibility_only)","explanation_zh":"收束波核對=([-25, 26], -1, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253049,"parameters":{"interval":[-25,26],"point":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-25,26],\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0050","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-feasible-point-audit；資料={\"interval\":[-26,27],\"point\":[0,1]}。請依 [interval,point,feasible,scope] 欄序回答。","answer":{"kind":"expression","value":"([-26, 27], 0, 是, feasibility_only)","explanation_zh":"收束波核對=([-26, 27], 0, 是, feasibility_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-feasible-point-audit","seed":202610253050,"parameters":{"interval":[-26,27],"point":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-feasible-point-audit","semantic_template":"qf-mod25-convexopt-feasible-point-audit/{\"interval\":[-26,27],\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0051","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[0,-12,-3],\"interval\":[-2,3],\"point\":[-3,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, -12, -3], [-2, 3], -3, 否, 33, evaluation_only)","explanation_zh":"收束波核對=([0, -12, -3], [-2, 3], -3, 否, 33, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253051,"parameters":{"coefficients":[0,-12,-3],"interval":[-2,3],"point":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[0,-12,-3],\"interval\":[-2,3],\"point\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0052","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[1,-11,-2],\"interval\":[-3,4],\"point\":[-2,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, -11, -2], [-3, 4], -2, 是, 24, evaluation_only)","explanation_zh":"收束波核對=([1, -11, -2], [-3, 4], -2, 是, 24, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253052,"parameters":{"coefficients":[1,-11,-2],"interval":[-3,4],"point":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[1,-11,-2],\"interval\":[-3,4],\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0053","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[2,-10,-1],\"interval\":[-4,5],\"point\":[-1,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, -10, -1], [-4, 5], -1, 是, 11, evaluation_only)","explanation_zh":"收束波核對=([2, -10, -1], [-4, 5], -1, 是, 11, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253053,"parameters":{"coefficients":[2,-10,-1],"interval":[-4,5],"point":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[2,-10,-1],\"interval\":[-4,5],\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0054","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[3,-9,0],\"interval\":[-5,6],\"point\":[0,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, -9, 0], [-5, 6], 0, 是, 0, evaluation_only)","explanation_zh":"收束波核對=([3, -9, 0], [-5, 6], 0, 是, 0, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253054,"parameters":{"coefficients":[3,-9,0],"interval":[-5,6],"point":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[3,-9,0],\"interval\":[-5,6],\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0055","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[0,-8,1],\"interval\":[-6,7],\"point\":[1,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, -8, 1], [-6, 7], 1, 是, -7, evaluation_only)","explanation_zh":"收束波核對=([0, -8, 1], [-6, 7], 1, 是, -7, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253055,"parameters":{"coefficients":[0,-8,1],"interval":[-6,7],"point":[1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[0,-8,1],\"interval\":[-6,7],\"point\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0056","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[1,-7,2],\"interval\":[-7,8],\"point\":[2,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, -7, 2], [-7, 8], 2, 是, -8, evaluation_only)","explanation_zh":"收束波核對=([1, -7, 2], [-7, 8], 2, 是, -8, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253056,"parameters":{"coefficients":[1,-7,2],"interval":[-7,8],"point":[2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[1,-7,2],\"interval\":[-7,8],\"point\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0057","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[2,-6,3],\"interval\":[-8,9],\"point\":[3,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, -6, 3], [-8, 9], 3, 是, 3, evaluation_only)","explanation_zh":"收束波核對=([2, -6, 3], [-8, 9], 3, 是, 3, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253057,"parameters":{"coefficients":[2,-6,3],"interval":[-8,9],"point":[3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[2,-6,3],\"interval\":[-8,9],\"point\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0058","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[3,-5,-3],\"interval\":[-9,10],\"point\":[-3,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, -5, -3], [-9, 10], -3, 是, 39, evaluation_only)","explanation_zh":"收束波核對=([3, -5, -3], [-9, 10], -3, 是, 39, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253058,"parameters":{"coefficients":[3,-5,-3],"interval":[-9,10],"point":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[3,-5,-3],\"interval\":[-9,10],\"point\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0059","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[0,-4,-2],\"interval\":[-10,11],\"point\":[-2,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, -4, -2], [-10, 11], -2, 是, 6, evaluation_only)","explanation_zh":"收束波核對=([0, -4, -2], [-10, 11], -2, 是, 6, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253059,"parameters":{"coefficients":[0,-4,-2],"interval":[-10,11],"point":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[0,-4,-2],\"interval\":[-10,11],\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261025-r03-convex-optimization-problem-0064","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[1,1,3],\"interval\":[-15,16],\"point\":[3,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 3], [-15, 16], 3, 是, 15, evaluation_only)","explanation_zh":"收束波核對=([1, 1, 3], [-15, 16], 3, 是, 15, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253064,"parameters":{"coefficients":[1,1,3],"interval":[-15,16],"point":[3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[1,1,3],\"interval\":[-15,16],\"point\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0065","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[2,2,-3],\"interval\":[-16,17],\"point\":[-3,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, 2, -3], [-16, 17], -3, 是, 9, evaluation_only)","explanation_zh":"收束波核對=([2, 2, -3], [-16, 17], -3, 是, 9, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253065,"parameters":{"coefficients":[2,2,-3],"interval":[-16,17],"point":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[2,2,-3],\"interval\":[-16,17],\"point\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0066","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[3,3,-2],\"interval\":[-17,18],\"point\":[-2,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, 3, -2], [-17, 18], -2, 是, 4, evaluation_only)","explanation_zh":"收束波核對=([3, 3, -2], [-17, 18], -2, 是, 4, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253066,"parameters":{"coefficients":[3,3,-2],"interval":[-17,18],"point":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[3,3,-2],\"interval\":[-17,18],\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0067","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[0,4,-1],\"interval\":[-18,19],\"point\":[-1,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 4, -1], [-18, 19], -1, 是, -5, evaluation_only)","explanation_zh":"收束波核對=([0, 4, -1], [-18, 19], -1, 是, -5, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253067,"parameters":{"coefficients":[0,4,-1],"interval":[-18,19],"point":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[0,4,-1],\"interval\":[-18,19],\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0068","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[1,5,0],\"interval\":[-19,20],\"point\":[0,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, 5, 0], [-19, 20], 0, 是, 0, evaluation_only)","explanation_zh":"收束波核對=([1, 5, 0], [-19, 20], 0, 是, 0, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253068,"parameters":{"coefficients":[1,5,0],"interval":[-19,20],"point":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[1,5,0],\"interval\":[-19,20],\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0069","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[2,6,1],\"interval\":[-20,21],\"point\":[1,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, 6, 1], [-20, 21], 1, 是, 9, evaluation_only)","explanation_zh":"收束波核對=([2, 6, 1], [-20, 21], 1, 是, 9, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253069,"parameters":{"coefficients":[2,6,1],"interval":[-20,21],"point":[1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[2,6,1],\"interval\":[-20,21],\"point\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0070","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[3,7,2],\"interval\":[-21,22],\"point\":[2,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, 7, 2], [-21, 22], 2, 是, 28, evaluation_only)","explanation_zh":"收束波核對=([3, 7, 2], [-21, 22], 2, 是, 28, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253070,"parameters":{"coefficients":[3,7,2],"interval":[-21,22],"point":[2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[3,7,2],\"interval\":[-21,22],\"point\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0071","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[0,8,3],\"interval\":[-22,23],\"point\":[3,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 8, 3], [-22, 23], 3, 是, 27, evaluation_only)","explanation_zh":"收束波核對=([0, 8, 3], [-22, 23], 3, 是, 27, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253071,"parameters":{"coefficients":[0,8,3],"interval":[-22,23],"point":[3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[0,8,3],\"interval\":[-22,23],\"point\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0072","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[1,9,-3],\"interval\":[-23,24],\"point\":[-3,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, 9, -3], [-23, 24], -3, 是, -21, evaluation_only)","explanation_zh":"收束波核對=([1, 9, -3], [-23, 24], -3, 是, -21, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253072,"parameters":{"coefficients":[1,9,-3],"interval":[-23,24],"point":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[1,9,-3],\"interval\":[-23,24],\"point\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0073","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[2,10,-2],\"interval\":[-24,25],\"point\":[-2,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, 10, -2], [-24, 25], -2, 是, -14, evaluation_only)","explanation_zh":"收束波核對=([2, 10, -2], [-24, 25], -2, 是, -14, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253073,"parameters":{"coefficients":[2,10,-2],"interval":[-24,25],"point":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[2,10,-2],\"interval\":[-24,25],\"point\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0074","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[3,11,-1],\"interval\":[-25,26],\"point\":[-1,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, 11, -1], [-25, 26], -1, 是, -9, evaluation_only)","explanation_zh":"收束波核對=([3, 11, -1], [-25, 26], -1, 是, -9, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253074,"parameters":{"coefficients":[3,11,-1],"interval":[-25,26],"point":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[3,11,-1],\"interval\":[-25,26],\"point\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0075","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-objective-at-feasible-point；資料={\"coefficients\":[0,12,0],\"interval\":[-26,27],\"point\":[0,1]}。請依 [coefficients,interval,point,feasible,value,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 12, 0], [-26, 27], 0, 是, 0, evaluation_only)","explanation_zh":"收束波核對=([0, 12, 0], [-26, 27], 0, 是, 0, evaluation_only)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-objective-at-feasible-point","seed":202610253075,"parameters":{"coefficients":[0,12,0],"interval":[-26,27],"point":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-objective-at-feasible-point","semantic_template":"qf-mod25-convexopt-objective-at-feasible-point/{\"coefficients\":[0,12,0],\"interval\":[-26,27],\"point\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0076","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[0,-12,-3],\"interval\":[-2,3],\"left\":[-2,1],\"right\":[-3,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, -12, -3], [-2, 3], -2, 是, 21, -3, 否, 33, not_comparable, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([0, -12, -3], [-2, 3], -2, 是, 21, -3, 否, 33, not_comparable, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253076,"parameters":{"coefficients":[0,-12,-3],"interval":[-2,3],"left":[-2,1],"right":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[0,-12,-3],\"interval\":[-2,3],\"left\":[-2,1],\"right\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0077","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[1,-11,-2],\"interval\":[-3,4],\"left\":[-1,1],\"right\":[-2,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, -11, -2], [-3, 4], -1, 是, 10, -2, 是, 24, left_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([1, -11, -2], [-3, 4], -1, 是, 10, -2, 是, 24, left_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253077,"parameters":{"coefficients":[1,-11,-2],"interval":[-3,4],"left":[-1,1],"right":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[1,-11,-2],\"interval\":[-3,4],\"left\":[-1,1],\"right\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0078","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[2,-10,-1],\"interval\":[-4,5],\"left\":[0,1],\"right\":[-1,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, -10, -1], [-4, 5], 0, 是, -1, -1, 是, 11, left_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([2, -10, -1], [-4, 5], 0, 是, -1, -1, 是, 11, left_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253078,"parameters":{"coefficients":[2,-10,-1],"interval":[-4,5],"left":[0,1],"right":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[2,-10,-1],\"interval\":[-4,5],\"left\":[0,1],\"right\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0079","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[3,-9,0],\"interval\":[-5,6],\"left\":[1,1],\"right\":[0,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, -9, 0], [-5, 6], 1, 是, -6, 0, 是, 0, left_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([3, -9, 0], [-5, 6], 1, 是, -6, 0, 是, 0, left_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253079,"parameters":{"coefficients":[3,-9,0],"interval":[-5,6],"left":[1,1],"right":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[3,-9,0],\"interval\":[-5,6],\"left\":[1,1],\"right\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0080","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[0,-8,1],\"interval\":[-6,7],\"left\":[2,1],\"right\":[1,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, -8, 1], [-6, 7], 2, 是, -15, 1, 是, -7, left_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([0, -8, 1], [-6, 7], 2, 是, -15, 1, 是, -7, left_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253080,"parameters":{"coefficients":[0,-8,1],"interval":[-6,7],"left":[2,1],"right":[1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[0,-8,1],\"interval\":[-6,7],\"left\":[2,1],\"right\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0081","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[1,-7,2],\"interval\":[-7,8],\"left\":[-2,1],\"right\":[2,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, -7, 2], [-7, 8], -2, 是, 20, 2, 是, -8, right_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([1, -7, 2], [-7, 8], -2, 是, 20, 2, 是, -8, right_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253081,"parameters":{"coefficients":[1,-7,2],"interval":[-7,8],"left":[-2,1],"right":[2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[1,-7,2],\"interval\":[-7,8],\"left\":[-2,1],\"right\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0082","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[2,-6,3],\"interval\":[-8,9],\"left\":[-1,1],\"right\":[3,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, -6, 3], [-8, 9], -1, 是, 11, 3, 是, 3, right_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([2, -6, 3], [-8, 9], -1, 是, 11, 3, 是, 3, right_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253082,"parameters":{"coefficients":[2,-6,3],"interval":[-8,9],"left":[-1,1],"right":[3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[2,-6,3],\"interval\":[-8,9],\"left\":[-1,1],\"right\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0083","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[3,-5,-3],\"interval\":[-9,10],\"left\":[0,1],\"right\":[-3,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, -5, -3], [-9, 10], 0, 是, -3, -3, 是, 39, left_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([3, -5, -3], [-9, 10], 0, 是, -3, -3, 是, 39, left_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253083,"parameters":{"coefficients":[3,-5,-3],"interval":[-9,10],"left":[0,1],"right":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[3,-5,-3],\"interval\":[-9,10],\"left\":[0,1],\"right\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0084","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[0,-4,-2],\"interval\":[-10,11],\"left\":[1,1],\"right\":[-2,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, -4, -2], [-10, 11], 1, 是, -6, -2, 是, 6, left_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([0, -4, -2], [-10, 11], 1, 是, -6, -2, 是, 6, left_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253084,"parameters":{"coefficients":[0,-4,-2],"interval":[-10,11],"left":[1,1],"right":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[0,-4,-2],\"interval\":[-10,11],\"left\":[1,1],\"right\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0085","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[1,-3,-1],\"interval\":[-11,12],\"left\":[2,1],\"right\":[-1,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, -3, -1], [-11, 12], 2, 是, -3, -1, 是, 3, left_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([1, -3, -1], [-11, 12], 2, 是, -3, -1, 是, 3, left_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253085,"parameters":{"coefficients":[1,-3,-1],"interval":[-11,12],"left":[2,1],"right":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[1,-3,-1],\"interval\":[-11,12],\"left\":[2,1],\"right\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0086","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[2,-2,0],\"interval\":[-12,13],\"left\":[-2,1],\"right\":[0,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, -2, 0], [-12, 13], -2, 是, 12, 0, 是, 0, right_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([2, -2, 0], [-12, 13], -2, 是, 12, 0, 是, 0, right_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253086,"parameters":{"coefficients":[2,-2,0],"interval":[-12,13],"left":[-2,1],"right":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[2,-2,0],\"interval\":[-12,13],\"left\":[-2,1],\"right\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0087","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[3,-1,1],\"interval\":[-13,14],\"left\":[-1,1],\"right\":[1,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, -1, 1], [-13, 14], -1, 是, 5, 1, 是, 3, right_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([3, -1, 1], [-13, 14], -1, 是, 5, 1, 是, 3, right_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253087,"parameters":{"coefficients":[3,-1,1],"interval":[-13,14],"left":[-1,1],"right":[1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[3,-1,1],\"interval\":[-13,14],\"left\":[-1,1],\"right\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0088","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[0,0,2],\"interval\":[-14,15],\"left\":[0,1],\"right\":[2,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 2], [-14, 15], 0, 是, 2, 2, 是, 2, equal, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([0, 0, 2], [-14, 15], 0, 是, 2, 2, 是, 2, equal, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253088,"parameters":{"coefficients":[0,0,2],"interval":[-14,15],"left":[0,1],"right":[2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[0,0,2],\"interval\":[-14,15],\"left\":[0,1],\"right\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0089","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[1,1,3],\"interval\":[-15,16],\"left\":[1,1],\"right\":[3,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, 3], [-15, 16], 1, 是, 5, 3, 是, 15, left_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([1, 1, 3], [-15, 16], 1, 是, 5, 3, 是, 15, left_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253089,"parameters":{"coefficients":[1,1,3],"interval":[-15,16],"left":[1,1],"right":[3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[1,1,3],\"interval\":[-15,16],\"left\":[1,1],\"right\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0090","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[2,2,-3],\"interval\":[-16,17],\"left\":[2,1],\"right\":[-3,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, 2, -3], [-16, 17], 2, 是, 9, -3, 是, 9, equal, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([2, 2, -3], [-16, 17], 2, 是, 9, -3, 是, 9, equal, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253090,"parameters":{"coefficients":[2,2,-3],"interval":[-16,17],"left":[2,1],"right":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[2,2,-3],\"interval\":[-16,17],\"left\":[2,1],\"right\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0091","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[3,3,-2],\"interval\":[-17,18],\"left\":[-2,1],\"right\":[-2,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, 3, -2], [-17, 18], -2, 是, 4, -2, 是, 4, equal, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([3, 3, -2], [-17, 18], -2, 是, 4, -2, 是, 4, equal, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253091,"parameters":{"coefficients":[3,3,-2],"interval":[-17,18],"left":[-2,1],"right":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[3,3,-2],\"interval\":[-17,18],\"left\":[-2,1],\"right\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0092","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[0,4,-1],\"interval\":[-18,19],\"left\":[-1,1],\"right\":[-1,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 4, -1], [-18, 19], -1, 是, -5, -1, 是, -5, equal, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([0, 4, -1], [-18, 19], -1, 是, -5, -1, 是, -5, equal, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253092,"parameters":{"coefficients":[0,4,-1],"interval":[-18,19],"left":[-1,1],"right":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[0,4,-1],\"interval\":[-18,19],\"left\":[-1,1],\"right\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0093","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[1,5,0],\"interval\":[-19,20],\"left\":[0,1],\"right\":[0,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, 5, 0], [-19, 20], 0, 是, 0, 0, 是, 0, equal, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([1, 5, 0], [-19, 20], 0, 是, 0, 0, 是, 0, equal, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253093,"parameters":{"coefficients":[1,5,0],"interval":[-19,20],"left":[0,1],"right":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[1,5,0],\"interval\":[-19,20],\"left\":[0,1],\"right\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0094","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[2,6,1],\"interval\":[-20,21],\"left\":[1,1],\"right\":[1,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, 6, 1], [-20, 21], 1, 是, 9, 1, 是, 9, equal, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([2, 6, 1], [-20, 21], 1, 是, 9, 1, 是, 9, equal, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253094,"parameters":{"coefficients":[2,6,1],"interval":[-20,21],"left":[1,1],"right":[1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[2,6,1],\"interval\":[-20,21],\"left\":[1,1],\"right\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0095","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[3,7,2],\"interval\":[-21,22],\"left\":[2,1],\"right\":[2,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, 7, 2], [-21, 22], 2, 是, 28, 2, 是, 28, equal, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([3, 7, 2], [-21, 22], 2, 是, 28, 2, 是, 28, equal, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253095,"parameters":{"coefficients":[3,7,2],"interval":[-21,22],"left":[2,1],"right":[2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[3,7,2],\"interval\":[-21,22],\"left\":[2,1],\"right\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0096","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[0,8,3],\"interval\":[-22,23],\"left\":[-2,1],\"right\":[3,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 8, 3], [-22, 23], -2, 是, -13, 3, 是, 27, left_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([0, 8, 3], [-22, 23], -2, 是, -13, 3, 是, 27, left_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253096,"parameters":{"coefficients":[0,8,3],"interval":[-22,23],"left":[-2,1],"right":[3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[0,8,3],\"interval\":[-22,23],\"left\":[-2,1],\"right\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0097","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[1,9,-3],\"interval\":[-23,24],\"left\":[-1,1],\"right\":[-3,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([1, 9, -3], [-23, 24], -1, 是, -11, -3, 是, -21, right_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([1, 9, -3], [-23, 24], -1, 是, -11, -3, 是, -21, right_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253097,"parameters":{"coefficients":[1,9,-3],"interval":[-23,24],"left":[-1,1],"right":[-3,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[1,9,-3],\"interval\":[-23,24],\"left\":[-1,1],\"right\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0098","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[2,10,-2],\"interval\":[-24,25],\"left\":[0,1],\"right\":[-2,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([2, 10, -2], [-24, 25], 0, 是, -2, -2, 是, -14, right_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([2, 10, -2], [-24, 25], 0, 是, -2, -2, 是, -14, right_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253098,"parameters":{"coefficients":[2,10,-2],"interval":[-24,25],"left":[0,1],"right":[-2,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[2,10,-2],\"interval\":[-24,25],\"left\":[0,1],\"right\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0099","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[3,11,-1],\"interval\":[-25,26],\"left\":[1,1],\"right\":[-1,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([3, 11, -1], [-25, 26], 1, 是, 13, -1, 是, -9, right_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([3, 11, -1], [-25, 26], 1, 是, 13, -1, 是, -9, right_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253099,"parameters":{"coefficients":[3,11,-1],"interval":[-25,26],"left":[1,1],"right":[-1,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[3,11,-1],\"interval\":[-25,26],\"left\":[1,1],\"right\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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-20261025-r03-convex-optimization-problem-0100","batch_id":"batch-20261013-advance-20261025-r03-convex-optimization-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-convex-optimization-problem"],"title_zh":"凸最佳化問題","stem_zh":"凸目標資格與凸可行域資格分開。操作=convexopt-pairwise-feasible-comparison；資料={\"coefficients\":[0,12,0],\"interval\":[-26,27],\"left\":[2,1],\"right\":[0,1]}。請依 [coefficients,interval,left,left_feasible,left_value,right,right_feasible,right_value,relation,scope] 欄序回答。","answer":{"kind":"expression","value":"([0, 12, 0], [-26, 27], 2, 是, 24, 0, 是, 0, right_lower, pairwise_only_no_global_optimum_claim)","explanation_zh":"收束波核對=([0, 12, 0], [-26, 27], 2, 是, 24, 0, 是, 0, right_lower, pairwise_only_no_global_optimum_claim)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；只核可行性求值或兩候選比較；不宣稱通用求解器全域最優存在唯一KKT或收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["凸最佳化問題"]},"variant":{"family_id":"qf-mod25-convexopt-pairwise-feasible-comparison","seed":202610253100,"parameters":{"coefficients":[0,12,0],"interval":[-26,27],"left":[2,1],"right":[0,1],"domain":"Exact_interval_convex_optimization","operation":"convexopt-pairwise-feasible-comparison","semantic_template":"qf-mod25-convexopt-pairwise-feasible-comparison/{\"coefficients\":[0,12,0],\"interval\":[-26,27],\"left\":[2,1],\"right\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、BVP適定性、全域最佳解、Markov長期性、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"}}