{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0001","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[-3,-1,-3],\"right\":[-3,-2,-2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-3, -1, -3], [-3, -2, -2], [-6, -3, -5])","explanation_zh":"應用基礎核對=([-3, -1, -3], [-3, -2, -2], [-6, -3, -5])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205001,"parameters":{"left":[-3,-1,-3],"right":[-3,-2,-2],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[-3,-1,-3],\"right\":[-3,-2,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0002","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[-2,-1,-1],\"right\":[0,-1,-2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-2, -1, -1], [0, -1, -2], [-2, -2, -3])","explanation_zh":"應用基礎核對=([-2, -1, -1], [0, -1, -2], [-2, -2, -3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205002,"parameters":{"left":[-2,-1,-1],"right":[0,-1,-2],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[-2,-1,-1],\"right\":[0,-1,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0003","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[-1,-1,1],\"right\":[3,0,-2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-1, -1, 1], [3, 0, -2], [2, -1, -1])","explanation_zh":"應用基礎核對=([-1, -1, 1], [3, 0, -2], [2, -1, -1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205003,"parameters":{"left":[-1,-1,1],"right":[3,0,-2],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[-1,-1,1],\"right\":[3,0,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0011","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[0,0,3],\"right\":[-1,-2,0]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 3], [-1, -2, 0], [-1, -2, 3])","explanation_zh":"應用基礎核對=([0, 0, 3], [-1, -2, 0], [-1, -2, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205011,"parameters":{"left":[0,0,3],"right":[-1,-2,0],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[0,0,3],\"right\":[-1,-2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0012","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[1,0,-2],\"right\":[2,-1,0]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, -2], [2, -1, 0], [3, -1, -2])","explanation_zh":"應用基礎核對=([1, 0, -2], [2, -1, 0], [3, -1, -2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205012,"parameters":{"left":[1,0,-2],"right":[2,-1,0],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[1,0,-2],\"right\":[2,-1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0013","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[2,0,0],\"right\":[-2,0,0]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([2, 0, 0], [-2, 0, 0], [0, 0, 0])","explanation_zh":"應用基礎核對=([2, 0, 0], [-2, 0, 0], [0, 0, 0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205013,"parameters":{"left":[2,0,0],"right":[-2,0,0],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[2,0,0],\"right\":[-2,0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0014","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[3,0,2],\"right\":[1,1,0]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([3, 0, 2], [1, 1, 0], [4, 1, 2])","explanation_zh":"應用基礎核對=([3, 0, 2], [1, 1, 0], [4, 1, 2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205014,"parameters":{"left":[3,0,2],"right":[1,1,0],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[3,0,2],\"right\":[1,1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0015","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[-3,1,-3],\"right\":[-3,2,0]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-3, 1, -3], [-3, 2, 0], [-6, 3, -3])","explanation_zh":"應用基礎核對=([-3, 1, -3], [-3, 2, 0], [-6, 3, -3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205015,"parameters":{"left":[-3,1,-3],"right":[-3,2,0],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[-3,1,-3],\"right\":[-3,2,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0016","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[-2,1,-1],\"right\":[0,-2,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-2, 1, -1], [0, -2, 1], [-2, -1, 0])","explanation_zh":"應用基礎核對=([-2, 1, -1], [0, -2, 1], [-2, -1, 0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205016,"parameters":{"left":[-2,1,-1],"right":[0,-2,1],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[-2,1,-1],\"right\":[0,-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0017","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[-1,1,1],\"right\":[3,-1,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-1, 1, 1], [3, -1, 1], [2, 0, 2])","explanation_zh":"應用基礎核對=([-1, 1, 1], [3, -1, 1], [2, 0, 2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205017,"parameters":{"left":[-1,1,1],"right":[3,-1,1],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[-1,1,1],\"right\":[3,-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0018","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[0,1,3],\"right\":[-1,0,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3], [-1, 0, 1], [-1, 1, 4])","explanation_zh":"應用基礎核對=([0, 1, 3], [-1, 0, 1], [-1, 1, 4])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205018,"parameters":{"left":[0,1,3],"right":[-1,0,1],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[0,1,3],\"right\":[-1,0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0019","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[1,1,-2],\"right\":[2,1,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, -2], [2, 1, 1], [3, 2, -1])","explanation_zh":"應用基礎核對=([1, 1, -2], [2, 1, 1], [3, 2, -1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205019,"parameters":{"left":[1,1,-2],"right":[2,1,1],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[1,1,-2],\"right\":[2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0020","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[2,1,0],\"right\":[-2,2,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 0], [-2, 2, 1], [0, 3, 1])","explanation_zh":"應用基礎核對=([2, 1, 0], [-2, 2, 1], [0, 3, 1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205020,"parameters":{"left":[2,1,0],"right":[-2,2,1],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[2,1,0],\"right\":[-2,2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0021","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[3,1,2],\"right\":[1,-2,2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 2], [1, -2, 2], [4, -1, 4])","explanation_zh":"應用基礎核對=([3, 1, 2], [1, -2, 2], [4, -1, 4])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205021,"parameters":{"left":[3,1,2],"right":[1,-2,2],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[3,1,2],\"right\":[1,-2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0022","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[-3,2,-3],\"right\":[-3,-1,2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-3, 2, -3], [-3, -1, 2], [-6, 1, -1])","explanation_zh":"應用基礎核對=([-3, 2, -3], [-3, -1, 2], [-6, 1, -1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205022,"parameters":{"left":[-3,2,-3],"right":[-3,-1,2],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[-3,2,-3],\"right\":[-3,-1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0023","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-product；資料={\"left\":[-2,2,-1],\"right\":[0,0,2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2, -1], [0, 0, 2], [-2, 2, 1])","explanation_zh":"應用基礎核對=([-2, 2, -1], [0, 0, 2], [-2, 2, 1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-product","seed":202610205023,"parameters":{"left":[-2,2,-1],"right":[0,0,2],"domain":"Dimension_exponent_vectors","operation":"dimension-product","semantic_template":"qf-app20-dimension-product/{\"left\":[-2,2,-1],\"right\":[0,0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0032","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[3,-1,2],\"right\":[1,-1,-1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([3, -1, 2], [1, -1, -1], [2, 0, 3])","explanation_zh":"應用基礎核對=([3, -1, 2], [1, -1, -1], [2, 0, 3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205032,"parameters":{"left":[3,-1,2],"right":[1,-1,-1],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[3,-1,2],\"right\":[1,-1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0033","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[-3,0,-3],\"right\":[-3,0,-1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-3, 0, -3], [-3, 0, -1], [0, 0, -2])","explanation_zh":"應用基礎核對=([-3, 0, -3], [-3, 0, -1], [0, 0, -2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205033,"parameters":{"left":[-3,0,-3],"right":[-3,0,-1],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[-3,0,-3],\"right\":[-3,0,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0041","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[-2,1,-1],\"right\":[0,-2,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-2, 1, -1], [0, -2, 1], [-2, 3, -2])","explanation_zh":"應用基礎核對=([-2, 1, -1], [0, -2, 1], [-2, 3, -2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205041,"parameters":{"left":[-2,1,-1],"right":[0,-2,1],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[-2,1,-1],\"right\":[0,-2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0042","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[-1,1,1],\"right\":[3,-1,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-1, 1, 1], [3, -1, 1], [-4, 2, 0])","explanation_zh":"應用基礎核對=([-1, 1, 1], [3, -1, 1], [-4, 2, 0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205042,"parameters":{"left":[-1,1,1],"right":[3,-1,1],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[-1,1,1],\"right\":[3,-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0043","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[0,1,3],\"right\":[-1,0,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3], [-1, 0, 1], [1, 1, 2])","explanation_zh":"應用基礎核對=([0, 1, 3], [-1, 0, 1], [1, 1, 2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205043,"parameters":{"left":[0,1,3],"right":[-1,0,1],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[0,1,3],\"right\":[-1,0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0044","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[1,1,-2],\"right\":[2,1,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, -2], [2, 1, 1], [-1, 0, -3])","explanation_zh":"應用基礎核對=([1, 1, -2], [2, 1, 1], [-1, 0, -3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205044,"parameters":{"left":[1,1,-2],"right":[2,1,1],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[1,1,-2],\"right\":[2,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0045","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[2,1,0],\"right\":[-2,2,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 0], [-2, 2, 1], [4, -1, -1])","explanation_zh":"應用基礎核對=([2, 1, 0], [-2, 2, 1], [4, -1, -1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205045,"parameters":{"left":[2,1,0],"right":[-2,2,1],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[2,1,0],\"right\":[-2,2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0046","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[3,1,2],\"right\":[1,-2,2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 2], [1, -2, 2], [2, 3, 0])","explanation_zh":"應用基礎核對=([3, 1, 2], [1, -2, 2], [2, 3, 0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205046,"parameters":{"left":[3,1,2],"right":[1,-2,2],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[3,1,2],\"right\":[1,-2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0047","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[-3,2,-3],\"right\":[-3,-1,2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-3, 2, -3], [-3, -1, 2], [0, 3, -5])","explanation_zh":"應用基礎核對=([-3, 2, -3], [-3, -1, 2], [0, 3, -5])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205047,"parameters":{"left":[-3,2,-3],"right":[-3,-1,2],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[-3,2,-3],\"right\":[-3,-1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0048","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[-2,2,-1],\"right\":[0,0,2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2, -1], [0, 0, 2], [-2, 2, -3])","explanation_zh":"應用基礎核對=([-2, 2, -1], [0, 0, 2], [-2, 2, -3])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205048,"parameters":{"left":[-2,2,-1],"right":[0,0,2],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[-2,2,-1],\"right\":[0,0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0049","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[-1,2,1],\"right\":[3,1,2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2, 1], [3, 1, 2], [-4, 1, -1])","explanation_zh":"應用基礎核對=([-1, 2, 1], [3, 1, 2], [-4, 1, -1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205049,"parameters":{"left":[-1,2,1],"right":[3,1,2],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[-1,2,1],\"right\":[3,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0050","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-quotient；資料={\"left\":[0,2,3],\"right\":[-1,2,2]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3], [-1, 2, 2], [1, 0, 1])","explanation_zh":"應用基礎核對=([0, 2, 3], [-1, 2, 2], [1, 0, 1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-quotient","seed":202610205050,"parameters":{"left":[0,2,3],"right":[-1,2,2],"domain":"Dimension_exponent_vectors","operation":"dimension-quotient","semantic_template":"qf-app20-dimension-quotient/{\"left\":[0,2,3],\"right\":[-1,2,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0073","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-power；資料={\"base\":[-2,2,-1],\"exponent\":-2}。請依 [base,exponent,result] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2, -1], -2, [4, -4, 2])","explanation_zh":"應用基礎核對=([-2, 2, -1], -2, [4, -4, 2])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-power","seed":202610205073,"parameters":{"base":[-2,2,-1],"exponent":-2,"domain":"Dimension_exponent_vectors","operation":"dimension-power","semantic_template":"qf-app20-dimension-power/{\"base\":[-2,2,-1],\"exponent\":-2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0074","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-power；資料={\"base\":[-1,2,1],\"exponent\":-1}。請依 [base,exponent,result] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2, 1], -1, [1, -2, -1])","explanation_zh":"應用基礎核對=([-1, 2, 1], -1, [1, -2, -1])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-power","seed":202610205074,"parameters":{"base":[-1,2,1],"exponent":-1,"domain":"Dimension_exponent_vectors","operation":"dimension-power","semantic_template":"qf-app20-dimension-power/{\"base\":[-1,2,1],\"exponent\":-1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0075","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-power；資料={\"base\":[0,2,3],\"exponent\":0}。請依 [base,exponent,result] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3], 0, [0, 0, 0])","explanation_zh":"應用基礎核對=([0, 2, 3], 0, [0, 0, 0])；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-power","seed":202610205075,"parameters":{"base":[0,2,3],"exponent":0,"domain":"Dimension_exponent_vectors","operation":"dimension-power","semantic_template":"qf-app20-dimension-power/{\"base\":[0,2,3],\"exponent\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0076","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-3,-1,-3],\"right\":[-2,-1,-3]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-3, -1, -3], [-2, -1, -3], 否)","explanation_zh":"應用基礎核對=([-3, -1, -3], [-2, -1, -3], 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205076,"parameters":{"left":[-3,-1,-3],"right":[-2,-1,-3],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-3,-1,-3],\"right\":[-2,-1,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0077","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-2,-1,-1],\"right\":[-2,-1,-1]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-2, -1, -1], [-2, -1, -1], 是)","explanation_zh":"應用基礎核對=([-2, -1, -1], [-2, -1, -1], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205077,"parameters":{"left":[-2,-1,-1],"right":[-2,-1,-1],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-2,-1,-1],\"right\":[-2,-1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0078","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-1,-1,1],\"right\":[-1,-1,1]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-1, -1, 1], [-1, -1, 1], 是)","explanation_zh":"應用基礎核對=([-1, -1, 1], [-1, -1, 1], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205078,"parameters":{"left":[-1,-1,1],"right":[-1,-1,1],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-1,-1,1],\"right\":[-1,-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0079","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[0,-1,3],\"right\":[1,-1,3]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, -1, 3], [1, -1, 3], 否)","explanation_zh":"應用基礎核對=([0, -1, 3], [1, -1, 3], 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205079,"parameters":{"left":[0,-1,3],"right":[1,-1,3],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[0,-1,3],\"right\":[1,-1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0080","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[1,-1,-2],\"right\":[1,-1,-2]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([1, -1, -2], [1, -1, -2], 是)","explanation_zh":"應用基礎核對=([1, -1, -2], [1, -1, -2], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205080,"parameters":{"left":[1,-1,-2],"right":[1,-1,-2],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[1,-1,-2],\"right\":[1,-1,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0081","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[2,-1,0],\"right\":[2,-1,0]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([2, -1, 0], [2, -1, 0], 是)","explanation_zh":"應用基礎核對=([2, -1, 0], [2, -1, 0], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205081,"parameters":{"left":[2,-1,0],"right":[2,-1,0],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[2,-1,0],\"right\":[2,-1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0082","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[3,-1,2],\"right\":[4,-1,2]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([3, -1, 2], [4, -1, 2], 否)","explanation_zh":"應用基礎核對=([3, -1, 2], [4, -1, 2], 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205082,"parameters":{"left":[3,-1,2],"right":[4,-1,2],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[3,-1,2],\"right\":[4,-1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0083","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-3,0,-3],\"right\":[-3,0,-3]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-3, 0, -3], [-3, 0, -3], 是)","explanation_zh":"應用基礎核對=([-3, 0, -3], [-3, 0, -3], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205083,"parameters":{"left":[-3,0,-3],"right":[-3,0,-3],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-3,0,-3],\"right\":[-3,0,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0084","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-2,0,-1],\"right\":[-2,0,-1]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-2, 0, -1], [-2, 0, -1], 是)","explanation_zh":"應用基礎核對=([-2, 0, -1], [-2, 0, -1], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205084,"parameters":{"left":[-2,0,-1],"right":[-2,0,-1],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-2,0,-1],\"right\":[-2,0,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0085","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-1,0,1],\"right\":[0,0,1]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-1, 0, 1], [0, 0, 1], 否)","explanation_zh":"應用基礎核對=([-1, 0, 1], [0, 0, 1], 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205085,"parameters":{"left":[-1,0,1],"right":[0,0,1],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-1,0,1],\"right\":[0,0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0086","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[0,0,3],\"right\":[0,0,3]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 0, 3], [0, 0, 3], 是)","explanation_zh":"應用基礎核對=([0, 0, 3], [0, 0, 3], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205086,"parameters":{"left":[0,0,3],"right":[0,0,3],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[0,0,3],\"right\":[0,0,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0087","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[1,0,-2],\"right\":[1,0,-2]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([1, 0, -2], [1, 0, -2], 是)","explanation_zh":"應用基礎核對=([1, 0, -2], [1, 0, -2], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205087,"parameters":{"left":[1,0,-2],"right":[1,0,-2],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[1,0,-2],\"right\":[1,0,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0088","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[2,0,0],\"right\":[3,0,0]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([2, 0, 0], [3, 0, 0], 否)","explanation_zh":"應用基礎核對=([2, 0, 0], [3, 0, 0], 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205088,"parameters":{"left":[2,0,0],"right":[3,0,0],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[2,0,0],\"right\":[3,0,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0089","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[3,0,2],\"right\":[3,0,2]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([3, 0, 2], [3, 0, 2], 是)","explanation_zh":"應用基礎核對=([3, 0, 2], [3, 0, 2], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205089,"parameters":{"left":[3,0,2],"right":[3,0,2],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[3,0,2],\"right\":[3,0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0090","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-3,1,-3],\"right\":[-3,1,-3]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-3, 1, -3], [-3, 1, -3], 是)","explanation_zh":"應用基礎核對=([-3, 1, -3], [-3, 1, -3], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205090,"parameters":{"left":[-3,1,-3],"right":[-3,1,-3],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-3,1,-3],\"right\":[-3,1,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0091","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-2,1,-1],\"right\":[-1,1,-1]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-2, 1, -1], [-1, 1, -1], 否)","explanation_zh":"應用基礎核對=([-2, 1, -1], [-1, 1, -1], 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205091,"parameters":{"left":[-2,1,-1],"right":[-1,1,-1],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-2,1,-1],\"right\":[-1,1,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0092","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-1,1,1],\"right\":[-1,1,1]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-1, 1, 1], [-1, 1, 1], 是)","explanation_zh":"應用基礎核對=([-1, 1, 1], [-1, 1, 1], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205092,"parameters":{"left":[-1,1,1],"right":[-1,1,1],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-1,1,1],\"right\":[-1,1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0093","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[0,1,3],\"right\":[0,1,3]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3], [0, 1, 3], 是)","explanation_zh":"應用基礎核對=([0, 1, 3], [0, 1, 3], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205093,"parameters":{"left":[0,1,3],"right":[0,1,3],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[0,1,3],\"right\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0094","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[1,1,-2],\"right\":[2,1,-2]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([1, 1, -2], [2, 1, -2], 否)","explanation_zh":"應用基礎核對=([1, 1, -2], [2, 1, -2], 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205094,"parameters":{"left":[1,1,-2],"right":[2,1,-2],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[1,1,-2],\"right\":[2,1,-2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0095","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[2,1,0],\"right\":[2,1,0]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([2, 1, 0], [2, 1, 0], 是)","explanation_zh":"應用基礎核對=([2, 1, 0], [2, 1, 0], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205095,"parameters":{"left":[2,1,0],"right":[2,1,0],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[2,1,0],\"right\":[2,1,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0096","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[3,1,2],\"right\":[3,1,2]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([3, 1, 2], [3, 1, 2], 是)","explanation_zh":"應用基礎核對=([3, 1, 2], [3, 1, 2], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205096,"parameters":{"left":[3,1,2],"right":[3,1,2],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[3,1,2],\"right\":[3,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0097","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-3,2,-3],\"right\":[-2,2,-3]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-3, 2, -3], [-2, 2, -3], 否)","explanation_zh":"應用基礎核對=([-3, 2, -3], [-2, 2, -3], 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205097,"parameters":{"left":[-3,2,-3],"right":[-2,2,-3],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-3,2,-3],\"right\":[-2,2,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0098","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-2,2,-1],\"right\":[-2,2,-1]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-2, 2, -1], [-2, 2, -1], 是)","explanation_zh":"應用基礎核對=([-2, 2, -1], [-2, 2, -1], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205098,"parameters":{"left":[-2,2,-1],"right":[-2,2,-1],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-2,2,-1],\"right\":[-2,2,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0099","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[-1,2,1],\"right\":[-1,2,1]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([-1, 2, 1], [-1, 2, 1], 是)","explanation_zh":"應用基礎核對=([-1, 2, 1], [-1, 2, 1], 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205099,"parameters":{"left":[-1,2,1],"right":[-1,2,1],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[-1,2,1],\"right\":[-1,2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r05-dimensional-analysis-0100","batch_id":"batch-20261013-advance-20261020-r05-dimensional-analysis-foundations","language":"zh-Hant","source_mko_ids":["mko-dimensional-analysis"],"title_zh":"量綱指數向量","stem_zh":"基本量綱指數向量[L,M,T]。操作=dimension-equation-consistency；資料={\"left\":[0,2,3],\"right\":[1,2,3]}。請依 [left,right,consistent] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 3], [1, 2, 3], 否)","explanation_zh":"應用基礎核對=([0, 2, 3], [1, 2, 3], 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；量綱一致是必要而非充分條件；不證物理模型正確。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["量綱指數向量"]},"variant":{"family_id":"qf-app20-dimension-equation-consistency","seed":202610205100,"parameters":{"left":[0,2,3],"right":[1,2,3],"domain":"Dimension_exponent_vectors","operation":"dimension-equation-consistency","semantic_template":"qf-app20-dimension-equation-consistency/{\"left\":[0,2,3],\"right\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}