{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r05-finite-convex-combination-0001","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-12,0],[-10,2]],\"weights\":[[2,3],[2,3]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-12, 0], [-10, 2]], [2/3, 2/3], 是, 4/3, 否, 否)","explanation_zh":"依賴結構核對=([[-12, 0], [-10, 2]], [2/3, 2/3], 是, 4/3, 否, 否)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245001,"parameters":{"vectors":[[-12,0],[-10,2]],"weights":[[2,3],[2,3]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-12,0],[-10,2]],\"weights\":[[2,3],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0002","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-11,0],[-9,2]],\"weights\":[[2,4],[2,4]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-11, 0], [-9, 2]], [1/2, 1/2], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[-11, 0], [-9, 2]], [1/2, 1/2], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245002,"parameters":{"vectors":[[-11,0],[-9,2]],"weights":[[2,4],[2,4]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-11,0],[-9,2]],\"weights\":[[2,4],[2,4]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0003","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-10,0],[-8,2]],\"weights\":[[3,5],[2,5]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-10, 0], [-8, 2]], [3/5, 2/5], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[-10, 0], [-8, 2]], [3/5, 2/5], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245003,"parameters":{"vectors":[[-10,0],[-8,2]],"weights":[[3,5],[2,5]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-10,0],[-8,2]],\"weights\":[[3,5],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0004","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-9,0],[-7,2]],\"weights\":[[4,6],[2,6]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-9, 0], [-7, 2]], [2/3, 1/3], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[-9, 0], [-7, 2]], [2/3, 1/3], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245004,"parameters":{"vectors":[[-9,0],[-7,2]],"weights":[[4,6],[2,6]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-9,0],[-7,2]],\"weights\":[[4,6],[2,6]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0005","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-8,0],[-6,2]],\"weights\":[[5,7],[2,7]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-8, 0], [-6, 2]], [5/7, 2/7], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[-8, 0], [-6, 2]], [5/7, 2/7], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245005,"parameters":{"vectors":[[-8,0],[-6,2]],"weights":[[5,7],[2,7]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-8,0],[-6,2]],\"weights\":[[5,7],[2,7]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0006","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-7,0],[-5,2]],\"weights\":[[2,3],[2,3]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-7, 0], [-5, 2]], [2/3, 2/3], 是, 4/3, 否, 否)","explanation_zh":"依賴結構核對=([[-7, 0], [-5, 2]], [2/3, 2/3], 是, 4/3, 否, 否)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245006,"parameters":{"vectors":[[-7,0],[-5,2]],"weights":[[2,3],[2,3]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-7,0],[-5,2]],\"weights\":[[2,3],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0007","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-6,0],[-4,2]],\"weights\":[[7,9],[2,9]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-6, 0], [-4, 2]], [7/9, 2/9], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[-6, 0], [-4, 2]], [7/9, 2/9], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245007,"parameters":{"vectors":[[-6,0],[-4,2]],"weights":[[7,9],[2,9]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-6,0],[-4,2]],\"weights\":[[7,9],[2,9]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0008","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-5,0],[-3,2]],\"weights\":[[8,10],[2,10]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-5, 0], [-3, 2]], [4/5, 1/5], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[-5, 0], [-3, 2]], [4/5, 1/5], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245008,"parameters":{"vectors":[[-5,0],[-3,2]],"weights":[[8,10],[2,10]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-5,0],[-3,2]],\"weights\":[[8,10],[2,10]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0009","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-4,0],[-2,2]],\"weights\":[[9,11],[2,11]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-4, 0], [-2, 2]], [9/11, 2/11], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[-4, 0], [-2, 2]], [9/11, 2/11], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245009,"parameters":{"vectors":[[-4,0],[-2,2]],"weights":[[9,11],[2,11]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-4,0],[-2,2]],\"weights\":[[9,11],[2,11]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0010","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-3,0],[-1,2]],\"weights\":[[10,12],[2,12]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-3, 0], [-1, 2]], [5/6, 1/6], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[-3, 0], [-1, 2]], [5/6, 1/6], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245010,"parameters":{"vectors":[[-3,0],[-1,2]],"weights":[[10,12],[2,12]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-3,0],[-1,2]],\"weights\":[[10,12],[2,12]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0011","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-2,0],[0,2]],\"weights\":[[2,3],[2,3]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-2, 0], [0, 2]], [2/3, 2/3], 是, 4/3, 否, 否)","explanation_zh":"依賴結構核對=([[-2, 0], [0, 2]], [2/3, 2/3], 是, 4/3, 否, 否)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245011,"parameters":{"vectors":[[-2,0],[0,2]],"weights":[[2,3],[2,3]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-2,0],[0,2]],\"weights\":[[2,3],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0012","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[-1,0],[1,2]],\"weights\":[[12,14],[2,14]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0], [1, 2]], [6/7, 1/7], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[-1, 0], [1, 2]], [6/7, 1/7], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245012,"parameters":{"vectors":[[-1,0],[1,2]],"weights":[[12,14],[2,14]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[-1,0],[1,2]],\"weights\":[[12,14],[2,14]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0013","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[0,0],[2,2]],\"weights\":[[13,15],[2,15]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [2, 2]], [13/15, 2/15], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[0, 0], [2, 2]], [13/15, 2/15], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245013,"parameters":{"vectors":[[0,0],[2,2]],"weights":[[13,15],[2,15]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[0,0],[2,2]],\"weights\":[[13,15],[2,15]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0014","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[1,0],[3,2]],\"weights\":[[14,16],[2,16]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[1, 0], [3, 2]], [7/8, 1/8], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[1, 0], [3, 2]], [7/8, 1/8], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245014,"parameters":{"vectors":[[1,0],[3,2]],"weights":[[14,16],[2,16]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[1,0],[3,2]],\"weights\":[[14,16],[2,16]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0015","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[2,0],[4,2]],\"weights\":[[15,17],[2,17]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[2, 0], [4, 2]], [15/17, 2/17], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[2, 0], [4, 2]], [15/17, 2/17], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245015,"parameters":{"vectors":[[2,0],[4,2]],"weights":[[15,17],[2,17]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[2,0],[4,2]],\"weights\":[[15,17],[2,17]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0016","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[3,0],[5,2]],\"weights\":[[2,3],[2,3]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[3, 0], [5, 2]], [2/3, 2/3], 是, 4/3, 否, 否)","explanation_zh":"依賴結構核對=([[3, 0], [5, 2]], [2/3, 2/3], 是, 4/3, 否, 否)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245016,"parameters":{"vectors":[[3,0],[5,2]],"weights":[[2,3],[2,3]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[3,0],[5,2]],\"weights\":[[2,3],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0017","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[4,0],[6,2]],\"weights\":[[17,19],[2,19]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[4, 0], [6, 2]], [17/19, 2/19], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[4, 0], [6, 2]], [17/19, 2/19], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245017,"parameters":{"vectors":[[4,0],[6,2]],"weights":[[17,19],[2,19]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[4,0],[6,2]],\"weights\":[[17,19],[2,19]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0018","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[5,0],[7,2]],\"weights\":[[18,20],[2,20]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[5, 0], [7, 2]], [9/10, 1/10], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[5, 0], [7, 2]], [9/10, 1/10], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245018,"parameters":{"vectors":[[5,0],[7,2]],"weights":[[18,20],[2,20]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[5,0],[7,2]],\"weights\":[[18,20],[2,20]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0019","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[6,0],[8,2]],\"weights\":[[19,21],[2,21]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[6, 0], [8, 2]], [19/21, 2/21], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[6, 0], [8, 2]], [19/21, 2/21], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245019,"parameters":{"vectors":[[6,0],[8,2]],"weights":[[19,21],[2,21]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[6,0],[8,2]],\"weights\":[[19,21],[2,21]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0020","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[7,0],[9,2]],\"weights\":[[20,22],[2,22]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[7, 0], [9, 2]], [10/11, 1/11], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[7, 0], [9, 2]], [10/11, 1/11], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245020,"parameters":{"vectors":[[7,0],[9,2]],"weights":[[20,22],[2,22]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[7,0],[9,2]],\"weights\":[[20,22],[2,22]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0021","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[8,0],[10,2]],\"weights\":[[2,3],[2,3]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[8, 0], [10, 2]], [2/3, 2/3], 是, 4/3, 否, 否)","explanation_zh":"依賴結構核對=([[8, 0], [10, 2]], [2/3, 2/3], 是, 4/3, 否, 否)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245021,"parameters":{"vectors":[[8,0],[10,2]],"weights":[[2,3],[2,3]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[8,0],[10,2]],\"weights\":[[2,3],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0022","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[9,0],[11,2]],\"weights\":[[22,24],[2,24]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[9, 0], [11, 2]], [11/12, 1/12], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[9, 0], [11, 2]], [11/12, 1/12], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245022,"parameters":{"vectors":[[9,0],[11,2]],"weights":[[22,24],[2,24]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[9,0],[11,2]],\"weights\":[[22,24],[2,24]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0023","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[10,0],[12,2]],\"weights\":[[23,25],[2,25]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[10, 0], [12, 2]], [23/25, 2/25], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[10, 0], [12, 2]], [23/25, 2/25], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245023,"parameters":{"vectors":[[10,0],[12,2]],"weights":[[23,25],[2,25]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[10,0],[12,2]],\"weights\":[[23,25],[2,25]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0024","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[11,0],[13,2]],\"weights\":[[24,26],[2,26]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[11, 0], [13, 2]], [12/13, 1/13], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[11, 0], [13, 2]], [12/13, 1/13], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245024,"parameters":{"vectors":[[11,0],[13,2]],"weights":[[24,26],[2,26]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[11,0],[13,2]],\"weights\":[[24,26],[2,26]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0025","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-qualification；資料={\"vectors\":[[12,0],[14,2]],\"weights\":[[25,27],[2,27]]}。請依 [vectors,weights,nonnegative,sum,total_one,qualified] 欄序回答。","answer":{"kind":"expression","value":"([[12, 0], [14, 2]], [25/27, 2/27], 是, 1, 是, 是)","explanation_zh":"依賴結構核對=([[12, 0], [14, 2]], [25/27, 2/27], 是, 1, 是, 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-qualification","seed":202610245025,"parameters":{"vectors":[[12,0],[14,2]],"weights":[[25,27],[2,27]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-qualification","semantic_template":"qf-mod24-convcomb-qualification/{\"vectors\":[[12,0],[14,2]],\"weights\":[[25,27],[2,27]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0026","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-12,0],[-10,2]],\"weights\":[[1,3],[2,3]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-12, 0], [-10, 2]], [1/3, 2/3], [-32/3, 4/3])","explanation_zh":"依賴結構核對=([[-12, 0], [-10, 2]], [1/3, 2/3], [-32/3, 4/3])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245026,"parameters":{"vectors":[[-12,0],[-10,2]],"weights":[[1,3],[2,3]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-12,0],[-10,2]],\"weights\":[[1,3],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0027","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-11,0],[-9,2]],\"weights\":[[2,4],[2,4]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-11, 0], [-9, 2]], [1/2, 1/2], [-10, 1])","explanation_zh":"依賴結構核對=([[-11, 0], [-9, 2]], [1/2, 1/2], [-10, 1])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245027,"parameters":{"vectors":[[-11,0],[-9,2]],"weights":[[2,4],[2,4]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-11,0],[-9,2]],\"weights\":[[2,4],[2,4]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0028","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-10,0],[-8,2]],\"weights\":[[3,5],[2,5]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-10, 0], [-8, 2]], [3/5, 2/5], [-46/5, 4/5])","explanation_zh":"依賴結構核對=([[-10, 0], [-8, 2]], [3/5, 2/5], [-46/5, 4/5])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245028,"parameters":{"vectors":[[-10,0],[-8,2]],"weights":[[3,5],[2,5]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-10,0],[-8,2]],\"weights\":[[3,5],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0029","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-9,0],[-7,2]],\"weights\":[[4,6],[2,6]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-9, 0], [-7, 2]], [2/3, 1/3], [-25/3, 2/3])","explanation_zh":"依賴結構核對=([[-9, 0], [-7, 2]], [2/3, 1/3], [-25/3, 2/3])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245029,"parameters":{"vectors":[[-9,0],[-7,2]],"weights":[[4,6],[2,6]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-9,0],[-7,2]],\"weights\":[[4,6],[2,6]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0030","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-8,0],[-6,2]],\"weights\":[[5,7],[2,7]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-8, 0], [-6, 2]], [5/7, 2/7], [-52/7, 4/7])","explanation_zh":"依賴結構核對=([[-8, 0], [-6, 2]], [5/7, 2/7], [-52/7, 4/7])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245030,"parameters":{"vectors":[[-8,0],[-6,2]],"weights":[[5,7],[2,7]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-8,0],[-6,2]],\"weights\":[[5,7],[2,7]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0031","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-7,0],[-5,2]],\"weights\":[[6,8],[2,8]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-7, 0], [-5, 2]], [3/4, 1/4], [-13/2, 1/2])","explanation_zh":"依賴結構核對=([[-7, 0], [-5, 2]], [3/4, 1/4], [-13/2, 1/2])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245031,"parameters":{"vectors":[[-7,0],[-5,2]],"weights":[[6,8],[2,8]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-7,0],[-5,2]],\"weights\":[[6,8],[2,8]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0032","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-6,0],[-4,2]],\"weights\":[[7,9],[2,9]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-6, 0], [-4, 2]], [7/9, 2/9], [-50/9, 4/9])","explanation_zh":"依賴結構核對=([[-6, 0], [-4, 2]], [7/9, 2/9], [-50/9, 4/9])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245032,"parameters":{"vectors":[[-6,0],[-4,2]],"weights":[[7,9],[2,9]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-6,0],[-4,2]],\"weights\":[[7,9],[2,9]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0033","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-5,0],[-3,2]],\"weights\":[[8,10],[2,10]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-5, 0], [-3, 2]], [4/5, 1/5], [-23/5, 2/5])","explanation_zh":"依賴結構核對=([[-5, 0], [-3, 2]], [4/5, 1/5], [-23/5, 2/5])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245033,"parameters":{"vectors":[[-5,0],[-3,2]],"weights":[[8,10],[2,10]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-5,0],[-3,2]],\"weights\":[[8,10],[2,10]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0034","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-4,0],[-2,2]],\"weights\":[[9,11],[2,11]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-4, 0], [-2, 2]], [9/11, 2/11], [-40/11, 4/11])","explanation_zh":"依賴結構核對=([[-4, 0], [-2, 2]], [9/11, 2/11], [-40/11, 4/11])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245034,"parameters":{"vectors":[[-4,0],[-2,2]],"weights":[[9,11],[2,11]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-4,0],[-2,2]],\"weights\":[[9,11],[2,11]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0035","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-3,0],[-1,2]],\"weights\":[[10,12],[2,12]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-3, 0], [-1, 2]], [5/6, 1/6], [-8/3, 1/3])","explanation_zh":"依賴結構核對=([[-3, 0], [-1, 2]], [5/6, 1/6], [-8/3, 1/3])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245035,"parameters":{"vectors":[[-3,0],[-1,2]],"weights":[[10,12],[2,12]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-3,0],[-1,2]],\"weights\":[[10,12],[2,12]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0036","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-2,0],[0,2]],\"weights\":[[11,13],[2,13]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-2, 0], [0, 2]], [11/13, 2/13], [-22/13, 4/13])","explanation_zh":"依賴結構核對=([[-2, 0], [0, 2]], [11/13, 2/13], [-22/13, 4/13])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245036,"parameters":{"vectors":[[-2,0],[0,2]],"weights":[[11,13],[2,13]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-2,0],[0,2]],\"weights\":[[11,13],[2,13]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0037","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[-1,0],[1,2]],\"weights\":[[12,14],[2,14]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[-1, 0], [1, 2]], [6/7, 1/7], [-5/7, 2/7])","explanation_zh":"依賴結構核對=([[-1, 0], [1, 2]], [6/7, 1/7], [-5/7, 2/7])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245037,"parameters":{"vectors":[[-1,0],[1,2]],"weights":[[12,14],[2,14]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[-1,0],[1,2]],\"weights\":[[12,14],[2,14]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0038","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[0,0],[2,2]],\"weights\":[[13,15],[2,15]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [2, 2]], [13/15, 2/15], [4/15, 4/15])","explanation_zh":"依賴結構核對=([[0, 0], [2, 2]], [13/15, 2/15], [4/15, 4/15])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245038,"parameters":{"vectors":[[0,0],[2,2]],"weights":[[13,15],[2,15]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[0,0],[2,2]],\"weights\":[[13,15],[2,15]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0039","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[1,0],[3,2]],\"weights\":[[14,16],[2,16]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[1, 0], [3, 2]], [7/8, 1/8], [5/4, 1/4])","explanation_zh":"依賴結構核對=([[1, 0], [3, 2]], [7/8, 1/8], [5/4, 1/4])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245039,"parameters":{"vectors":[[1,0],[3,2]],"weights":[[14,16],[2,16]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[1,0],[3,2]],\"weights\":[[14,16],[2,16]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0040","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[2,0],[4,2]],\"weights\":[[15,17],[2,17]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[2, 0], [4, 2]], [15/17, 2/17], [38/17, 4/17])","explanation_zh":"依賴結構核對=([[2, 0], [4, 2]], [15/17, 2/17], [38/17, 4/17])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245040,"parameters":{"vectors":[[2,0],[4,2]],"weights":[[15,17],[2,17]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[2,0],[4,2]],\"weights\":[[15,17],[2,17]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0041","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[3,0],[5,2]],\"weights\":[[16,18],[2,18]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[3, 0], [5, 2]], [8/9, 1/9], [29/9, 2/9])","explanation_zh":"依賴結構核對=([[3, 0], [5, 2]], [8/9, 1/9], [29/9, 2/9])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245041,"parameters":{"vectors":[[3,0],[5,2]],"weights":[[16,18],[2,18]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[3,0],[5,2]],\"weights\":[[16,18],[2,18]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0042","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[4,0],[6,2]],\"weights\":[[17,19],[2,19]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[4, 0], [6, 2]], [17/19, 2/19], [80/19, 4/19])","explanation_zh":"依賴結構核對=([[4, 0], [6, 2]], [17/19, 2/19], [80/19, 4/19])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245042,"parameters":{"vectors":[[4,0],[6,2]],"weights":[[17,19],[2,19]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[4,0],[6,2]],\"weights\":[[17,19],[2,19]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0043","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[5,0],[7,2]],\"weights\":[[18,20],[2,20]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[5, 0], [7, 2]], [9/10, 1/10], [26/5, 1/5])","explanation_zh":"依賴結構核對=([[5, 0], [7, 2]], [9/10, 1/10], [26/5, 1/5])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245043,"parameters":{"vectors":[[5,0],[7,2]],"weights":[[18,20],[2,20]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[5,0],[7,2]],\"weights\":[[18,20],[2,20]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0044","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[6,0],[8,2]],\"weights\":[[19,21],[2,21]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[6, 0], [8, 2]], [19/21, 2/21], [130/21, 4/21])","explanation_zh":"依賴結構核對=([[6, 0], [8, 2]], [19/21, 2/21], [130/21, 4/21])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245044,"parameters":{"vectors":[[6,0],[8,2]],"weights":[[19,21],[2,21]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[6,0],[8,2]],\"weights\":[[19,21],[2,21]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0045","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[7,0],[9,2]],\"weights\":[[20,22],[2,22]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[7, 0], [9, 2]], [10/11, 1/11], [79/11, 2/11])","explanation_zh":"依賴結構核對=([[7, 0], [9, 2]], [10/11, 1/11], [79/11, 2/11])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245045,"parameters":{"vectors":[[7,0],[9,2]],"weights":[[20,22],[2,22]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[7,0],[9,2]],\"weights\":[[20,22],[2,22]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0046","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[8,0],[10,2]],\"weights\":[[21,23],[2,23]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[8, 0], [10, 2]], [21/23, 2/23], [188/23, 4/23])","explanation_zh":"依賴結構核對=([[8, 0], [10, 2]], [21/23, 2/23], [188/23, 4/23])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245046,"parameters":{"vectors":[[8,0],[10,2]],"weights":[[21,23],[2,23]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[8,0],[10,2]],\"weights\":[[21,23],[2,23]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0047","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[9,0],[11,2]],\"weights\":[[22,24],[2,24]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[9, 0], [11, 2]], [11/12, 1/12], [55/6, 1/6])","explanation_zh":"依賴結構核對=([[9, 0], [11, 2]], [11/12, 1/12], [55/6, 1/6])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245047,"parameters":{"vectors":[[9,0],[11,2]],"weights":[[22,24],[2,24]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[9,0],[11,2]],\"weights\":[[22,24],[2,24]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0048","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[10,0],[12,2]],\"weights\":[[23,25],[2,25]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[10, 0], [12, 2]], [23/25, 2/25], [254/25, 4/25])","explanation_zh":"依賴結構核對=([[10, 0], [12, 2]], [23/25, 2/25], [254/25, 4/25])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245048,"parameters":{"vectors":[[10,0],[12,2]],"weights":[[23,25],[2,25]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[10,0],[12,2]],\"weights\":[[23,25],[2,25]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0049","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[11,0],[13,2]],\"weights\":[[24,26],[2,26]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[11, 0], [13, 2]], [12/13, 1/13], [145/13, 2/13])","explanation_zh":"依賴結構核對=([[11, 0], [13, 2]], [12/13, 1/13], [145/13, 2/13])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245049,"parameters":{"vectors":[[11,0],[13,2]],"weights":[[24,26],[2,26]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[11,0],[13,2]],\"weights\":[[24,26],[2,26]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0050","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-weighted-point；資料={\"vectors\":[[12,0],[14,2]],\"weights\":[[25,27],[2,27]]}。請依 [vectors,weights,point] 欄序回答。","answer":{"kind":"expression","value":"([[12, 0], [14, 2]], [25/27, 2/27], [328/27, 4/27])","explanation_zh":"依賴結構核對=([[12, 0], [14, 2]], [25/27, 2/27], [328/27, 4/27])；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-weighted-point","seed":202610245050,"parameters":{"vectors":[[12,0],[14,2]],"weights":[[25,27],[2,27]],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-weighted-point","semantic_template":"qf-mod24-convcomb-weighted-point/{\"vectors\":[[12,0],[14,2]],\"weights\":[[25,27],[2,27]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0051","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-12,0],\"right\":[-9,3],\"lambda\":[1,3]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-12, 0], [-9, 3], 1/3, 是, [-10, 2], 是)","explanation_zh":"依賴結構核對=([-12, 0], [-9, 3], 1/3, 是, [-10, 2], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245051,"parameters":{"left":[-12,0],"right":[-9,3],"lambda":[1,3],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[1,3],\"left\":[-12,0],\"right\":[-9,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0052","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-11,0],\"right\":[-8,3],\"lambda\":[2,4]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-11, 0], [-8, 3], 1/2, 是, [-19/2, 3/2], 是)","explanation_zh":"依賴結構核對=([-11, 0], [-8, 3], 1/2, 是, [-19/2, 3/2], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245052,"parameters":{"left":[-11,0],"right":[-8,3],"lambda":[2,4],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[2,4],\"left\":[-11,0],\"right\":[-8,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0053","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-10,0],\"right\":[-7,3],\"lambda\":[3,5]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-10, 0], [-7, 3], 3/5, 是, [-44/5, 6/5], 是)","explanation_zh":"依賴結構核對=([-10, 0], [-7, 3], 3/5, 是, [-44/5, 6/5], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245053,"parameters":{"left":[-10,0],"right":[-7,3],"lambda":[3,5],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[3,5],\"left\":[-10,0],\"right\":[-7,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0054","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-9,0],\"right\":[-6,3],\"lambda\":[4,6]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-9, 0], [-6, 3], 2/3, 是, [-8, 1], 是)","explanation_zh":"依賴結構核對=([-9, 0], [-6, 3], 2/3, 是, [-8, 1], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245054,"parameters":{"left":[-9,0],"right":[-6,3],"lambda":[4,6],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[4,6],\"left\":[-9,0],\"right\":[-6,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0055","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-8,0],\"right\":[-5,3],\"lambda\":[5,7]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-8, 0], [-5, 3], 5/7, 是, [-50/7, 6/7], 是)","explanation_zh":"依賴結構核對=([-8, 0], [-5, 3], 5/7, 是, [-50/7, 6/7], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245055,"parameters":{"left":[-8,0],"right":[-5,3],"lambda":[5,7],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[5,7],\"left\":[-8,0],\"right\":[-5,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0056","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-7,0],\"right\":[-4,3],\"lambda\":[6,8]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-7, 0], [-4, 3], 3/4, 是, [-25/4, 3/4], 是)","explanation_zh":"依賴結構核對=([-7, 0], [-4, 3], 3/4, 是, [-25/4, 3/4], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245056,"parameters":{"left":[-7,0],"right":[-4,3],"lambda":[6,8],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[6,8],\"left\":[-7,0],\"right\":[-4,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0057","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-6,0],\"right\":[-3,3],\"lambda\":[7,9]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-6, 0], [-3, 3], 7/9, 是, [-16/3, 2/3], 是)","explanation_zh":"依賴結構核對=([-6, 0], [-3, 3], 7/9, 是, [-16/3, 2/3], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245057,"parameters":{"left":[-6,0],"right":[-3,3],"lambda":[7,9],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[7,9],\"left\":[-6,0],\"right\":[-3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0058","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-5,0],\"right\":[-2,3],\"lambda\":[8,10]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-5, 0], [-2, 3], 4/5, 是, [-22/5, 3/5], 是)","explanation_zh":"依賴結構核對=([-5, 0], [-2, 3], 4/5, 是, [-22/5, 3/5], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245058,"parameters":{"left":[-5,0],"right":[-2,3],"lambda":[8,10],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[8,10],\"left\":[-5,0],\"right\":[-2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0059","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-4,0],\"right\":[-1,3],\"lambda\":[9,11]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-4, 0], [-1, 3], 9/11, 是, [-38/11, 6/11], 是)","explanation_zh":"依賴結構核對=([-4, 0], [-1, 3], 9/11, 是, [-38/11, 6/11], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245059,"parameters":{"left":[-4,0],"right":[-1,3],"lambda":[9,11],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[9,11],\"left\":[-4,0],\"right\":[-1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0060","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-3,0],\"right\":[0,3],\"lambda\":[10,12]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-3, 0], [0, 3], 5/6, 是, [-5/2, 1/2], 是)","explanation_zh":"依賴結構核對=([-3, 0], [0, 3], 5/6, 是, [-5/2, 1/2], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245060,"parameters":{"left":[-3,0],"right":[0,3],"lambda":[10,12],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[10,12],\"left\":[-3,0],\"right\":[0,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0061","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-2,0],\"right\":[1,3],\"lambda\":[11,13]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-2, 0], [1, 3], 11/13, 是, [-20/13, 6/13], 是)","explanation_zh":"依賴結構核對=([-2, 0], [1, 3], 11/13, 是, [-20/13, 6/13], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245061,"parameters":{"left":[-2,0],"right":[1,3],"lambda":[11,13],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[11,13],\"left\":[-2,0],\"right\":[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0062","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[-1,0],\"right\":[2,3],\"lambda\":[12,14]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([-1, 0], [2, 3], 6/7, 是, [-4/7, 3/7], 是)","explanation_zh":"依賴結構核對=([-1, 0], [2, 3], 6/7, 是, [-4/7, 3/7], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245062,"parameters":{"left":[-1,0],"right":[2,3],"lambda":[12,14],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[12,14],\"left\":[-1,0],\"right\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0063","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[0,0],\"right\":[3,3],\"lambda\":[13,15]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([0, 0], [3, 3], 13/15, 是, [2/5, 2/5], 是)","explanation_zh":"依賴結構核對=([0, 0], [3, 3], 13/15, 是, [2/5, 2/5], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245063,"parameters":{"left":[0,0],"right":[3,3],"lambda":[13,15],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[13,15],\"left\":[0,0],\"right\":[3,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0064","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[1,0],\"right\":[4,3],\"lambda\":[14,16]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([1, 0], [4, 3], 7/8, 是, [11/8, 3/8], 是)","explanation_zh":"依賴結構核對=([1, 0], [4, 3], 7/8, 是, [11/8, 3/8], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245064,"parameters":{"left":[1,0],"right":[4,3],"lambda":[14,16],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[14,16],\"left\":[1,0],\"right\":[4,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0065","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[2,0],\"right\":[5,3],\"lambda\":[15,17]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([2, 0], [5, 3], 15/17, 是, [40/17, 6/17], 是)","explanation_zh":"依賴結構核對=([2, 0], [5, 3], 15/17, 是, [40/17, 6/17], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245065,"parameters":{"left":[2,0],"right":[5,3],"lambda":[15,17],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[15,17],\"left\":[2,0],\"right\":[5,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0066","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[3,0],\"right\":[6,3],\"lambda\":[16,18]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], [6, 3], 8/9, 是, [10/3, 1/3], 是)","explanation_zh":"依賴結構核對=([3, 0], [6, 3], 8/9, 是, [10/3, 1/3], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245066,"parameters":{"left":[3,0],"right":[6,3],"lambda":[16,18],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[16,18],\"left\":[3,0],\"right\":[6,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0067","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[4,0],\"right\":[7,3],\"lambda\":[17,19]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([4, 0], [7, 3], 17/19, 是, [82/19, 6/19], 是)","explanation_zh":"依賴結構核對=([4, 0], [7, 3], 17/19, 是, [82/19, 6/19], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245067,"parameters":{"left":[4,0],"right":[7,3],"lambda":[17,19],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[17,19],\"left\":[4,0],\"right\":[7,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0068","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[5,0],\"right\":[8,3],\"lambda\":[18,20]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([5, 0], [8, 3], 9/10, 是, [53/10, 3/10], 是)","explanation_zh":"依賴結構核對=([5, 0], [8, 3], 9/10, 是, [53/10, 3/10], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245068,"parameters":{"left":[5,0],"right":[8,3],"lambda":[18,20],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[18,20],\"left\":[5,0],\"right\":[8,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0069","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[6,0],\"right\":[9,3],\"lambda\":[19,21]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([6, 0], [9, 3], 19/21, 是, [44/7, 2/7], 是)","explanation_zh":"依賴結構核對=([6, 0], [9, 3], 19/21, 是, [44/7, 2/7], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245069,"parameters":{"left":[6,0],"right":[9,3],"lambda":[19,21],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[19,21],\"left\":[6,0],\"right\":[9,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0070","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[7,0],\"right\":[10,3],\"lambda\":[20,22]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([7, 0], [10, 3], 10/11, 是, [80/11, 3/11], 是)","explanation_zh":"依賴結構核對=([7, 0], [10, 3], 10/11, 是, [80/11, 3/11], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245070,"parameters":{"left":[7,0],"right":[10,3],"lambda":[20,22],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[20,22],\"left\":[7,0],\"right\":[10,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0071","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[8,0],\"right\":[11,3],\"lambda\":[21,23]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([8, 0], [11, 3], 21/23, 是, [190/23, 6/23], 是)","explanation_zh":"依賴結構核對=([8, 0], [11, 3], 21/23, 是, [190/23, 6/23], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245071,"parameters":{"left":[8,0],"right":[11,3],"lambda":[21,23],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[21,23],\"left\":[8,0],\"right\":[11,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0072","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[9,0],\"right\":[12,3],\"lambda\":[22,24]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([9, 0], [12, 3], 11/12, 是, [37/4, 1/4], 是)","explanation_zh":"依賴結構核對=([9, 0], [12, 3], 11/12, 是, [37/4, 1/4], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245072,"parameters":{"left":[9,0],"right":[12,3],"lambda":[22,24],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[22,24],\"left\":[9,0],\"right\":[12,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0073","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[10,0],\"right\":[13,3],\"lambda\":[23,25]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([10, 0], [13, 3], 23/25, 是, [256/25, 6/25], 是)","explanation_zh":"依賴結構核對=([10, 0], [13, 3], 23/25, 是, [256/25, 6/25], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245073,"parameters":{"left":[10,0],"right":[13,3],"lambda":[23,25],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[23,25],\"left\":[10,0],\"right\":[13,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0074","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[11,0],\"right\":[14,3],\"lambda\":[24,26]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([11, 0], [14, 3], 12/13, 是, [146/13, 3/13], 是)","explanation_zh":"依賴結構核對=([11, 0], [14, 3], 12/13, 是, [146/13, 3/13], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245074,"parameters":{"left":[11,0],"right":[14,3],"lambda":[24,26],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[24,26],\"left\":[11,0],\"right\":[14,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0075","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-two-point；資料={\"left\":[12,0],\"right\":[15,3],\"lambda\":[25,27]}。請依 [left,right,lambda,in_unit_interval,point,convex_combination] 欄序回答。","answer":{"kind":"expression","value":"([12, 0], [15, 3], 25/27, 是, [110/9, 2/9], 是)","explanation_zh":"依賴結構核對=([12, 0], [15, 3], 25/27, 是, [110/9, 2/9], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-two-point","seed":202610245075,"parameters":{"left":[12,0],"right":[15,3],"lambda":[25,27],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-two-point","semantic_template":"qf-mod24-convcomb-two-point/{\"lambda\":[25,27],\"left\":[12,0],\"right\":[15,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0076","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[3,0]],\"weights\":[[1,3],[2,3]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [3, 0]], [1/3, 2/3], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [3, 0]], [1/3, 2/3], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245076,"parameters":{"vectors":[[0,0],[3,0]],"weights":[[1,3],[2,3]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[3,0]],\"weights\":[[1,3],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0077","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[4,0]],\"weights\":[[2,4],[2,4]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [4, 0]], [1/2, 1/2], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [4, 0]], [1/2, 1/2], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245077,"parameters":{"vectors":[[0,0],[4,0]],"weights":[[2,4],[2,4]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[4,0]],\"weights\":[[2,4],[2,4]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0078","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[5,0]],\"weights\":[[3,5],[2,5]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [5, 0]], [3/5, 2/5], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [5, 0]], [3/5, 2/5], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245078,"parameters":{"vectors":[[0,0],[5,0]],"weights":[[3,5],[2,5]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[5,0]],\"weights\":[[3,5],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0079","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[6,0]],\"weights\":[[4,6],[2,6]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [6, 0]], [2/3, 1/3], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [6, 0]], [2/3, 1/3], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245079,"parameters":{"vectors":[[0,0],[6,0]],"weights":[[4,6],[2,6]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[6,0]],\"weights\":[[4,6],[2,6]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0080","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[7,0]],\"weights\":[[5,7],[2,7]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [7, 0]], [5/7, 2/7], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [7, 0]], [5/7, 2/7], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245080,"parameters":{"vectors":[[0,0],[7,0]],"weights":[[5,7],[2,7]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[7,0]],\"weights\":[[5,7],[2,7]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0081","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[8,0]],\"weights\":[[6,8],[2,8]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [8, 0]], [3/4, 1/4], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [8, 0]], [3/4, 1/4], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245081,"parameters":{"vectors":[[0,0],[8,0]],"weights":[[6,8],[2,8]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[8,0]],\"weights\":[[6,8],[2,8]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0082","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[9,0]],\"weights\":[[7,9],[2,9]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [9, 0]], [7/9, 2/9], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [9, 0]], [7/9, 2/9], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245082,"parameters":{"vectors":[[0,0],[9,0]],"weights":[[7,9],[2,9]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[9,0]],\"weights\":[[7,9],[2,9]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0083","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[10,0]],\"weights\":[[8,10],[2,10]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [10, 0]], [4/5, 1/5], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [10, 0]], [4/5, 1/5], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245083,"parameters":{"vectors":[[0,0],[10,0]],"weights":[[8,10],[2,10]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[10,0]],\"weights\":[[8,10],[2,10]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0084","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[11,0]],\"weights\":[[9,11],[2,11]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [11, 0]], [9/11, 2/11], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [11, 0]], [9/11, 2/11], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245084,"parameters":{"vectors":[[0,0],[11,0]],"weights":[[9,11],[2,11]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[11,0]],\"weights\":[[9,11],[2,11]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0085","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[12,0]],\"weights\":[[10,12],[2,12]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [12, 0]], [5/6, 1/6], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [12, 0]], [5/6, 1/6], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245085,"parameters":{"vectors":[[0,0],[12,0]],"weights":[[10,12],[2,12]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[12,0]],\"weights\":[[10,12],[2,12]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0086","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[13,0]],\"weights\":[[11,13],[2,13]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [13, 0]], [11/13, 2/13], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [13, 0]], [11/13, 2/13], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245086,"parameters":{"vectors":[[0,0],[13,0]],"weights":[[11,13],[2,13]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[13,0]],\"weights\":[[11,13],[2,13]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0087","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[14,0]],\"weights\":[[12,14],[2,14]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [14, 0]], [6/7, 1/7], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [14, 0]], [6/7, 1/7], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245087,"parameters":{"vectors":[[0,0],[14,0]],"weights":[[12,14],[2,14]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[14,0]],\"weights\":[[12,14],[2,14]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0088","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[15,0]],\"weights\":[[13,15],[2,15]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [15, 0]], [13/15, 2/15], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [15, 0]], [13/15, 2/15], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245088,"parameters":{"vectors":[[0,0],[15,0]],"weights":[[13,15],[2,15]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[15,0]],\"weights\":[[13,15],[2,15]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0089","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[16,0]],\"weights\":[[14,16],[2,16]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [16, 0]], [7/8, 1/8], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [16, 0]], [7/8, 1/8], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245089,"parameters":{"vectors":[[0,0],[16,0]],"weights":[[14,16],[2,16]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[16,0]],\"weights\":[[14,16],[2,16]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0090","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[17,0]],\"weights\":[[15,17],[2,17]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [17, 0]], [15/17, 2/17], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [17, 0]], [15/17, 2/17], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245090,"parameters":{"vectors":[[0,0],[17,0]],"weights":[[15,17],[2,17]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[17,0]],\"weights\":[[15,17],[2,17]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0091","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[18,0]],\"weights\":[[16,18],[2,18]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [18, 0]], [8/9, 1/9], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [18, 0]], [8/9, 1/9], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245091,"parameters":{"vectors":[[0,0],[18,0]],"weights":[[16,18],[2,18]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[18,0]],\"weights\":[[16,18],[2,18]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0092","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[19,0]],\"weights\":[[17,19],[2,19]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [19, 0]], [17/19, 2/19], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [19, 0]], [17/19, 2/19], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245092,"parameters":{"vectors":[[0,0],[19,0]],"weights":[[17,19],[2,19]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[19,0]],\"weights\":[[17,19],[2,19]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0093","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[20,0]],\"weights\":[[18,20],[2,20]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [20, 0]], [9/10, 1/10], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [20, 0]], [9/10, 1/10], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245093,"parameters":{"vectors":[[0,0],[20,0]],"weights":[[18,20],[2,20]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[20,0]],\"weights\":[[18,20],[2,20]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0094","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[21,0]],\"weights\":[[19,21],[2,21]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [21, 0]], [19/21, 2/21], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [21, 0]], [19/21, 2/21], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245094,"parameters":{"vectors":[[0,0],[21,0]],"weights":[[19,21],[2,21]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[21,0]],\"weights\":[[19,21],[2,21]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0095","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[22,0]],\"weights\":[[20,22],[2,22]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [22, 0]], [10/11, 1/11], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [22, 0]], [10/11, 1/11], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245095,"parameters":{"vectors":[[0,0],[22,0]],"weights":[[20,22],[2,22]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[22,0]],\"weights\":[[20,22],[2,22]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0096","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[23,0]],\"weights\":[[21,23],[2,23]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [23, 0]], [21/23, 2/23], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [23, 0]], [21/23, 2/23], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245096,"parameters":{"vectors":[[0,0],[23,0]],"weights":[[21,23],[2,23]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[23,0]],\"weights\":[[21,23],[2,23]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0097","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[24,0]],\"weights\":[[22,24],[2,24]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [24, 0]], [11/12, 1/12], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [24, 0]], [11/12, 1/12], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245097,"parameters":{"vectors":[[0,0],[24,0]],"weights":[[22,24],[2,24]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[24,0]],\"weights\":[[22,24],[2,24]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0098","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[25,0]],\"weights\":[[23,25],[2,25]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [25, 0]], [23/25, 2/25], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [25, 0]], [23/25, 2/25], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245098,"parameters":{"vectors":[[0,0],[25,0]],"weights":[[23,25],[2,25]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[25,0]],\"weights\":[[23,25],[2,25]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0099","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[26,0]],\"weights\":[[24,26],[2,26]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [26, 0]], [12/13, 1/13], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [26, 0]], [12/13, 1/13], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245099,"parameters":{"vectors":[[0,0],[26,0]],"weights":[[24,26],[2,26]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[26,0]],\"weights\":[[24,26],[2,26]]}"}},"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、Markov長期性、PDE適定性、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-20261024-r05-finite-convex-combination-0100","batch_id":"batch-20261013-advance-20261024-r05-finite-convex-combination-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-convex-combination"],"title_zh":"有限凸組合","stem_zh":"有限非空向量列與精確有理權重。操作=convcomb-witness-audit；資料={\"vectors\":[[0,0],[27,0]],\"weights\":[[25,27],[2,27]],\"target\":[2,0]}。請依 [vectors,weights,target,point,matches] 欄序回答。","answer":{"kind":"expression","value":"([[0, 0], [27, 0]], [25/27, 2/27], [2, 0], [2, 0], 是)","explanation_zh":"依賴結構核對=([[0, 0], [27, 0]], [25/27, 2/27], [2, 0], [2, 0], 是)；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；凸權重允許零但不得為負且總和必須精確為1；不由凸組合主張座標唯一性。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["有限凸組合"]},"variant":{"family_id":"qf-mod24-convcomb-witness-audit","seed":202610245100,"parameters":{"vectors":[[0,0],[27,0]],"weights":[[25,27],[2,27]],"target":[2,0],"domain":"Exact_finite_rational_convex_combinations","operation":"convcomb-witness-audit","semantic_template":"qf-mod24-convcomb-witness-audit/{\"target\":[2,0],\"vectors\":[[0,0],[27,0]],\"weights\":[[25,27],[2,27]]}"}},"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、Markov長期性、PDE適定性、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"}}