{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0001","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-12,-3],\"right\":[-2,-9]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-12, -3], [-2, -9], [-14, -12])","explanation_zh":"結構基礎核對=([-12, -3], [-2, -9], [-14, -12])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223001,"parameters":{"left":[-12,-3],"right":[-2,-9],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-12,-3],\"right\":[-2,-9]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0002","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-11,-2],\"right\":[-1,-7]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-11, -2], [-1, -7], [-12, -9])","explanation_zh":"結構基礎核對=([-11, -2], [-1, -7], [-12, -9])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223002,"parameters":{"left":[-11,-2],"right":[-1,-7],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-11,-2],\"right\":[-1,-7]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0003","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-10,-1],\"right\":[0,-5]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-10, -1], [0, -5], [-10, -6])","explanation_zh":"結構基礎核對=([-10, -1], [0, -5], [-10, -6])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223003,"parameters":{"left":[-10,-1],"right":[0,-5],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-10,-1],\"right\":[0,-5]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0004","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-9,0],\"right\":[1,-3]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-9, 0], [1, -3], [-8, -3])","explanation_zh":"結構基礎核對=([-9, 0], [1, -3], [-8, -3])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223004,"parameters":{"left":[-9,0],"right":[1,-3],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-9,0],\"right\":[1,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0005","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-8,1],\"right\":[2,-1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-8, 1], [2, -1], [-6, 0])","explanation_zh":"結構基礎核對=([-8, 1], [2, -1], [-6, 0])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223005,"parameters":{"left":[-8,1],"right":[2,-1],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-8,1],\"right\":[2,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0006","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-7,2],\"right\":[-2,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-7, 2], [-2, 1], [-9, 3])","explanation_zh":"結構基礎核對=([-7, 2], [-2, 1], [-9, 3])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223006,"parameters":{"left":[-7,2],"right":[-2,1],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-7,2],\"right\":[-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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0007","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-6,3],\"right\":[-1,3]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-6, 3], [-1, 3], [-7, 6])","explanation_zh":"結構基礎核對=([-6, 3], [-1, 3], [-7, 6])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223007,"parameters":{"left":[-6,3],"right":[-1,3],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-6,3],\"right\":[-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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0008","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-5,-3],\"right\":[0,5]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-5, -3], [0, 5], [-5, 2])","explanation_zh":"結構基礎核對=([-5, -3], [0, 5], [-5, 2])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223008,"parameters":{"left":[-5,-3],"right":[0,5],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-5,-3],\"right\":[0,5]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0009","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-4,-2],\"right\":[1,7]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-4, -2], [1, 7], [-3, 5])","explanation_zh":"結構基礎核對=([-4, -2], [1, 7], [-3, 5])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223009,"parameters":{"left":[-4,-2],"right":[1,7],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-4,-2],\"right\":[1,7]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0010","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-3,-1],\"right\":[2,9]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-3, -1], [2, 9], [-1, 8])","explanation_zh":"結構基礎核對=([-3, -1], [2, 9], [-1, 8])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223010,"parameters":{"left":[-3,-1],"right":[2,9],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-3,-1],\"right\":[2,9]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0011","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-2,0],\"right\":[-2,11]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-2, 0], [-2, 11], [-4, 11])","explanation_zh":"結構基礎核對=([-2, 0], [-2, 11], [-4, 11])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223011,"parameters":{"left":[-2,0],"right":[-2,11],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-2,0],\"right\":[-2,11]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0012","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[-1,1],\"right\":[-1,13]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-1, 1], [-1, 13], [-2, 14])","explanation_zh":"結構基礎核對=([-1, 1], [-1, 13], [-2, 14])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223012,"parameters":{"left":[-1,1],"right":[-1,13],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[-1,1],\"right\":[-1,13]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0013","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[0,2],\"right\":[0,15]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [0, 15], [0, 17])","explanation_zh":"結構基礎核對=([0, 2], [0, 15], [0, 17])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223013,"parameters":{"left":[0,2],"right":[0,15],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[0,2],\"right\":[0,15]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0014","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[1,3],\"right\":[1,17]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [1, 17], [2, 20])","explanation_zh":"結構基礎核對=([1, 3], [1, 17], [2, 20])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223014,"parameters":{"left":[1,3],"right":[1,17],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[1,3],\"right\":[1,17]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0015","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[2,-3],\"right\":[2,19]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([2, -3], [2, 19], [4, 16])","explanation_zh":"結構基礎核對=([2, -3], [2, 19], [4, 16])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223015,"parameters":{"left":[2,-3],"right":[2,19],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[2,-3],\"right\":[2,19]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0016","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[3,-2],\"right\":[-2,21]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([3, -2], [-2, 21], [1, 19])","explanation_zh":"結構基礎核對=([3, -2], [-2, 21], [1, 19])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223016,"parameters":{"left":[3,-2],"right":[-2,21],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[3,-2],\"right\":[-2,21]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0017","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[4,-1],\"right\":[-1,23]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([4, -1], [-1, 23], [3, 22])","explanation_zh":"結構基礎核對=([4, -1], [-1, 23], [3, 22])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223017,"parameters":{"left":[4,-1],"right":[-1,23],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[4,-1],\"right\":[-1,23]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0018","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[5,0],\"right\":[0,25]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([5, 0], [0, 25], [5, 25])","explanation_zh":"結構基礎核對=([5, 0], [0, 25], [5, 25])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223018,"parameters":{"left":[5,0],"right":[0,25],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[5,0],\"right\":[0,25]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0019","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[6,1],\"right\":[1,27]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([6, 1], [1, 27], [7, 28])","explanation_zh":"結構基礎核對=([6, 1], [1, 27], [7, 28])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223019,"parameters":{"left":[6,1],"right":[1,27],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[6,1],\"right\":[1,27]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0020","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[7,2],\"right\":[2,29]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([7, 2], [2, 29], [9, 31])","explanation_zh":"結構基礎核對=([7, 2], [2, 29], [9, 31])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223020,"parameters":{"left":[7,2],"right":[2,29],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[7,2],\"right\":[2,29]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0021","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[8,3],\"right\":[-2,31]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([8, 3], [-2, 31], [6, 34])","explanation_zh":"結構基礎核對=([8, 3], [-2, 31], [6, 34])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223021,"parameters":{"left":[8,3],"right":[-2,31],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[8,3],\"right\":[-2,31]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0022","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[9,-3],\"right\":[-1,33]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([9, -3], [-1, 33], [8, 30])","explanation_zh":"結構基礎核對=([9, -3], [-1, 33], [8, 30])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223022,"parameters":{"left":[9,-3],"right":[-1,33],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[9,-3],\"right\":[-1,33]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0023","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[10,-2],\"right\":[0,35]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([10, -2], [0, 35], [10, 33])","explanation_zh":"結構基礎核對=([10, -2], [0, 35], [10, 33])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223023,"parameters":{"left":[10,-2],"right":[0,35],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[10,-2],\"right\":[0,35]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0024","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[11,-1],\"right\":[1,37]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([11, -1], [1, 37], [12, 36])","explanation_zh":"結構基礎核對=([11, -1], [1, 37], [12, 36])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223024,"parameters":{"left":[11,-1],"right":[1,37],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[11,-1],\"right\":[1,37]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0025","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-addition；資料={\"left\":[12,0],\"right\":[2,39]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([12, 0], [2, 39], [14, 39])","explanation_zh":"結構基礎核對=([12, 0], [2, 39], [14, 39])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-addition","seed":202610223025,"parameters":{"left":[12,0],"right":[2,39],"domain":"Integer_pair_complex_arithmetic","operation":"complex-addition","semantic_template":"qf-str22-complex-addition/{\"left\":[12,0],\"right\":[2,39]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0026","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-12,-3],\"right\":[-2,-9]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-12, -3], [-2, -9], [-10, 6])","explanation_zh":"結構基礎核對=([-12, -3], [-2, -9], [-10, 6])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223026,"parameters":{"left":[-12,-3],"right":[-2,-9],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-12,-3],\"right\":[-2,-9]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0027","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-11,-2],\"right\":[-1,-7]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-11, -2], [-1, -7], [-10, 5])","explanation_zh":"結構基礎核對=([-11, -2], [-1, -7], [-10, 5])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223027,"parameters":{"left":[-11,-2],"right":[-1,-7],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-11,-2],\"right\":[-1,-7]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0028","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-10,-1],\"right\":[0,-5]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-10, -1], [0, -5], [-10, 4])","explanation_zh":"結構基礎核對=([-10, -1], [0, -5], [-10, 4])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223028,"parameters":{"left":[-10,-1],"right":[0,-5],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-10,-1],\"right\":[0,-5]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0029","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-9,0],\"right\":[1,-3]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-9, 0], [1, -3], [-10, 3])","explanation_zh":"結構基礎核對=([-9, 0], [1, -3], [-10, 3])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223029,"parameters":{"left":[-9,0],"right":[1,-3],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-9,0],\"right\":[1,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0030","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-8,1],\"right\":[2,-1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-8, 1], [2, -1], [-10, 2])","explanation_zh":"結構基礎核對=([-8, 1], [2, -1], [-10, 2])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223030,"parameters":{"left":[-8,1],"right":[2,-1],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-8,1],\"right\":[2,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0031","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-7,2],\"right\":[-2,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-7, 2], [-2, 1], [-5, 1])","explanation_zh":"結構基礎核對=([-7, 2], [-2, 1], [-5, 1])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223031,"parameters":{"left":[-7,2],"right":[-2,1],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-7,2],\"right\":[-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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0032","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-6,3],\"right\":[-1,3]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-6, 3], [-1, 3], [-5, 0])","explanation_zh":"結構基礎核對=([-6, 3], [-1, 3], [-5, 0])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223032,"parameters":{"left":[-6,3],"right":[-1,3],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-6,3],\"right\":[-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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0033","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-5,-3],\"right\":[0,5]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-5, -3], [0, 5], [-5, -8])","explanation_zh":"結構基礎核對=([-5, -3], [0, 5], [-5, -8])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223033,"parameters":{"left":[-5,-3],"right":[0,5],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-5,-3],\"right\":[0,5]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0034","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-4,-2],\"right\":[1,7]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-4, -2], [1, 7], [-5, -9])","explanation_zh":"結構基礎核對=([-4, -2], [1, 7], [-5, -9])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223034,"parameters":{"left":[-4,-2],"right":[1,7],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-4,-2],\"right\":[1,7]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0035","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-3,-1],\"right\":[2,9]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-3, -1], [2, 9], [-5, -10])","explanation_zh":"結構基礎核對=([-3, -1], [2, 9], [-5, -10])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223035,"parameters":{"left":[-3,-1],"right":[2,9],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-3,-1],\"right\":[2,9]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0036","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-2,0],\"right\":[-2,11]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-2, 0], [-2, 11], [0, -11])","explanation_zh":"結構基礎核對=([-2, 0], [-2, 11], [0, -11])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223036,"parameters":{"left":[-2,0],"right":[-2,11],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-2,0],\"right\":[-2,11]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0037","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[-1,1],\"right\":[-1,13]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-1, 1], [-1, 13], [0, -12])","explanation_zh":"結構基礎核對=([-1, 1], [-1, 13], [0, -12])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223037,"parameters":{"left":[-1,1],"right":[-1,13],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[-1,1],\"right\":[-1,13]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0038","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[0,2],\"right\":[0,15]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [0, 15], [0, -13])","explanation_zh":"結構基礎核對=([0, 2], [0, 15], [0, -13])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223038,"parameters":{"left":[0,2],"right":[0,15],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[0,2],\"right\":[0,15]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0039","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[1,3],\"right\":[1,17]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [1, 17], [0, -14])","explanation_zh":"結構基礎核對=([1, 3], [1, 17], [0, -14])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223039,"parameters":{"left":[1,3],"right":[1,17],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[1,3],\"right\":[1,17]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0040","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[2,-3],\"right\":[2,19]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([2, -3], [2, 19], [0, -22])","explanation_zh":"結構基礎核對=([2, -3], [2, 19], [0, -22])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223040,"parameters":{"left":[2,-3],"right":[2,19],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[2,-3],\"right\":[2,19]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0041","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[3,-2],\"right\":[-2,21]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([3, -2], [-2, 21], [5, -23])","explanation_zh":"結構基礎核對=([3, -2], [-2, 21], [5, -23])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223041,"parameters":{"left":[3,-2],"right":[-2,21],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[3,-2],\"right\":[-2,21]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0042","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[4,-1],\"right\":[-1,23]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([4, -1], [-1, 23], [5, -24])","explanation_zh":"結構基礎核對=([4, -1], [-1, 23], [5, -24])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223042,"parameters":{"left":[4,-1],"right":[-1,23],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[4,-1],\"right\":[-1,23]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0043","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[5,0],\"right\":[0,25]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([5, 0], [0, 25], [5, -25])","explanation_zh":"結構基礎核對=([5, 0], [0, 25], [5, -25])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223043,"parameters":{"left":[5,0],"right":[0,25],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[5,0],\"right\":[0,25]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0044","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[6,1],\"right\":[1,27]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([6, 1], [1, 27], [5, -26])","explanation_zh":"結構基礎核對=([6, 1], [1, 27], [5, -26])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223044,"parameters":{"left":[6,1],"right":[1,27],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[6,1],\"right\":[1,27]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0045","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[7,2],\"right\":[2,29]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([7, 2], [2, 29], [5, -27])","explanation_zh":"結構基礎核對=([7, 2], [2, 29], [5, -27])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223045,"parameters":{"left":[7,2],"right":[2,29],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[7,2],\"right\":[2,29]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0046","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[8,3],\"right\":[-2,31]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([8, 3], [-2, 31], [10, -28])","explanation_zh":"結構基礎核對=([8, 3], [-2, 31], [10, -28])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223046,"parameters":{"left":[8,3],"right":[-2,31],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[8,3],\"right\":[-2,31]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0047","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[9,-3],\"right\":[-1,33]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([9, -3], [-1, 33], [10, -36])","explanation_zh":"結構基礎核對=([9, -3], [-1, 33], [10, -36])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223047,"parameters":{"left":[9,-3],"right":[-1,33],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[9,-3],\"right\":[-1,33]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0048","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[10,-2],\"right\":[0,35]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([10, -2], [0, 35], [10, -37])","explanation_zh":"結構基礎核對=([10, -2], [0, 35], [10, -37])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223048,"parameters":{"left":[10,-2],"right":[0,35],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[10,-2],\"right\":[0,35]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0049","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[11,-1],\"right\":[1,37]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([11, -1], [1, 37], [10, -38])","explanation_zh":"結構基礎核對=([11, -1], [1, 37], [10, -38])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223049,"parameters":{"left":[11,-1],"right":[1,37],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[11,-1],\"right\":[1,37]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0050","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-subtraction；資料={\"left\":[12,0],\"right\":[2,39]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([12, 0], [2, 39], [10, -39])","explanation_zh":"結構基礎核對=([12, 0], [2, 39], [10, -39])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-subtraction","seed":202610223050,"parameters":{"left":[12,0],"right":[2,39],"domain":"Integer_pair_complex_arithmetic","operation":"complex-subtraction","semantic_template":"qf-str22-complex-subtraction/{\"left\":[12,0],\"right\":[2,39]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0051","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-12,-3],\"right\":[-2,-9]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-12, -3], [-2, -9], [-3, 114])","explanation_zh":"結構基礎核對=([-12, -3], [-2, -9], [-3, 114])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223051,"parameters":{"left":[-12,-3],"right":[-2,-9],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-12,-3],\"right\":[-2,-9]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0052","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-11,-2],\"right\":[-1,-7]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-11, -2], [-1, -7], [-3, 79])","explanation_zh":"結構基礎核對=([-11, -2], [-1, -7], [-3, 79])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223052,"parameters":{"left":[-11,-2],"right":[-1,-7],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-11,-2],\"right\":[-1,-7]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0053","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-10,-1],\"right\":[0,-5]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-10, -1], [0, -5], [-5, 50])","explanation_zh":"結構基礎核對=([-10, -1], [0, -5], [-5, 50])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223053,"parameters":{"left":[-10,-1],"right":[0,-5],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-10,-1],\"right\":[0,-5]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0054","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-9,0],\"right\":[1,-3]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-9, 0], [1, -3], [-9, 27])","explanation_zh":"結構基礎核對=([-9, 0], [1, -3], [-9, 27])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223054,"parameters":{"left":[-9,0],"right":[1,-3],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-9,0],\"right\":[1,-3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0055","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-8,1],\"right\":[2,-1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-8, 1], [2, -1], [-15, 10])","explanation_zh":"結構基礎核對=([-8, 1], [2, -1], [-15, 10])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223055,"parameters":{"left":[-8,1],"right":[2,-1],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-8,1],\"right\":[2,-1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0056","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-7,2],\"right\":[-2,1]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-7, 2], [-2, 1], [12, -11])","explanation_zh":"結構基礎核對=([-7, 2], [-2, 1], [12, -11])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223056,"parameters":{"left":[-7,2],"right":[-2,1],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-7,2],\"right\":[-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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0057","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-6,3],\"right\":[-1,3]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-6, 3], [-1, 3], [-3, -21])","explanation_zh":"結構基礎核對=([-6, 3], [-1, 3], [-3, -21])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223057,"parameters":{"left":[-6,3],"right":[-1,3],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-6,3],\"right\":[-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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0058","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-5,-3],\"right\":[0,5]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-5, -3], [0, 5], [15, -25])","explanation_zh":"結構基礎核對=([-5, -3], [0, 5], [15, -25])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223058,"parameters":{"left":[-5,-3],"right":[0,5],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-5,-3],\"right\":[0,5]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0059","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-4,-2],\"right\":[1,7]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-4, -2], [1, 7], [10, -30])","explanation_zh":"結構基礎核對=([-4, -2], [1, 7], [10, -30])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223059,"parameters":{"left":[-4,-2],"right":[1,7],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-4,-2],\"right\":[1,7]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0060","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-3,-1],\"right\":[2,9]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-3, -1], [2, 9], [3, -29])","explanation_zh":"結構基礎核對=([-3, -1], [2, 9], [3, -29])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223060,"parameters":{"left":[-3,-1],"right":[2,9],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-3,-1],\"right\":[2,9]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0061","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-2,0],\"right\":[-2,11]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-2, 0], [-2, 11], [4, -22])","explanation_zh":"結構基礎核對=([-2, 0], [-2, 11], [4, -22])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223061,"parameters":{"left":[-2,0],"right":[-2,11],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-2,0],\"right\":[-2,11]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0062","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[-1,1],\"right\":[-1,13]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([-1, 1], [-1, 13], [-12, -14])","explanation_zh":"結構基礎核對=([-1, 1], [-1, 13], [-12, -14])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223062,"parameters":{"left":[-1,1],"right":[-1,13],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[-1,1],\"right\":[-1,13]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0063","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[0,2],\"right\":[0,15]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [0, 15], [-30, 0])","explanation_zh":"結構基礎核對=([0, 2], [0, 15], [-30, 0])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223063,"parameters":{"left":[0,2],"right":[0,15],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[0,2],\"right\":[0,15]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0064","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[1,3],\"right\":[1,17]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [1, 17], [-50, 20])","explanation_zh":"結構基礎核對=([1, 3], [1, 17], [-50, 20])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223064,"parameters":{"left":[1,3],"right":[1,17],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[1,3],\"right\":[1,17]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0065","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[2,-3],\"right\":[2,19]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([2, -3], [2, 19], [61, 32])","explanation_zh":"結構基礎核對=([2, -3], [2, 19], [61, 32])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223065,"parameters":{"left":[2,-3],"right":[2,19],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[2,-3],\"right\":[2,19]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0066","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[3,-2],\"right\":[-2,21]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([3, -2], [-2, 21], [36, 67])","explanation_zh":"結構基礎核對=([3, -2], [-2, 21], [36, 67])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223066,"parameters":{"left":[3,-2],"right":[-2,21],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[3,-2],\"right\":[-2,21]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0067","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[4,-1],\"right\":[-1,23]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([4, -1], [-1, 23], [19, 93])","explanation_zh":"結構基礎核對=([4, -1], [-1, 23], [19, 93])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223067,"parameters":{"left":[4,-1],"right":[-1,23],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[4,-1],\"right\":[-1,23]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0068","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[5,0],\"right\":[0,25]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([5, 0], [0, 25], [0, 125])","explanation_zh":"結構基礎核對=([5, 0], [0, 25], [0, 125])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223068,"parameters":{"left":[5,0],"right":[0,25],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[5,0],\"right\":[0,25]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0069","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[6,1],\"right\":[1,27]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([6, 1], [1, 27], [-21, 163])","explanation_zh":"結構基礎核對=([6, 1], [1, 27], [-21, 163])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223069,"parameters":{"left":[6,1],"right":[1,27],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[6,1],\"right\":[1,27]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0070","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[7,2],\"right\":[2,29]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([7, 2], [2, 29], [-44, 207])","explanation_zh":"結構基礎核對=([7, 2], [2, 29], [-44, 207])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223070,"parameters":{"left":[7,2],"right":[2,29],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[7,2],\"right\":[2,29]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0071","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[8,3],\"right\":[-2,31]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([8, 3], [-2, 31], [-109, 242])","explanation_zh":"結構基礎核對=([8, 3], [-2, 31], [-109, 242])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223071,"parameters":{"left":[8,3],"right":[-2,31],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[8,3],\"right\":[-2,31]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0072","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[9,-3],\"right\":[-1,33]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([9, -3], [-1, 33], [90, 300])","explanation_zh":"結構基礎核對=([9, -3], [-1, 33], [90, 300])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223072,"parameters":{"left":[9,-3],"right":[-1,33],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[9,-3],\"right\":[-1,33]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0073","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[10,-2],\"right\":[0,35]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([10, -2], [0, 35], [70, 350])","explanation_zh":"結構基礎核對=([10, -2], [0, 35], [70, 350])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223073,"parameters":{"left":[10,-2],"right":[0,35],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[10,-2],\"right\":[0,35]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0074","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[11,-1],\"right\":[1,37]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([11, -1], [1, 37], [48, 406])","explanation_zh":"結構基礎核對=([11, -1], [1, 37], [48, 406])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223074,"parameters":{"left":[11,-1],"right":[1,37],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[11,-1],\"right\":[1,37]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0075","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-multiplication；資料={\"left\":[12,0],\"right\":[2,39]}。請依 [left,right,result] 欄序回答。","answer":{"kind":"expression","value":"([12, 0], [2, 39], [24, 468])","explanation_zh":"結構基礎核對=([12, 0], [2, 39], [24, 468])；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-multiplication","seed":202610223075,"parameters":{"left":[12,0],"right":[2,39],"domain":"Integer_pair_complex_arithmetic","operation":"complex-multiplication","semantic_template":"qf-str22-complex-multiplication/{\"left\":[12,0],\"right\":[2,39]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0076","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-12,1],\"real_candidate\":-11}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-12, 1], -11, 否, 否)","explanation_zh":"結構基礎核對=([-12, 1], -11, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223076,"parameters":{"value":[-12,1],"real_candidate":-11,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-11,\"value\":[-12,1]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0077","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-11,0],\"real_candidate\":-11}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-11, 0], -11, 是, 是)","explanation_zh":"結構基礎核對=([-11, 0], -11, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223077,"parameters":{"value":[-11,0],"real_candidate":-11,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-11,\"value\":[-11,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0078","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-10,0],\"real_candidate\":-10}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-10, 0], -10, 是, 是)","explanation_zh":"結構基礎核對=([-10, 0], -10, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223078,"parameters":{"value":[-10,0],"real_candidate":-10,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-10,\"value\":[-10,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0079","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-9,0],\"real_candidate\":-8}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-9, 0], -8, 是, 否)","explanation_zh":"結構基礎核對=([-9, 0], -8, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223079,"parameters":{"value":[-9,0],"real_candidate":-8,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-8,\"value\":[-9,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0080","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-8,1],\"real_candidate\":-8}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-8, 1], -8, 否, 否)","explanation_zh":"結構基礎核對=([-8, 1], -8, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223080,"parameters":{"value":[-8,1],"real_candidate":-8,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-8,\"value\":[-8,1]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0081","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-7,0],\"real_candidate\":-7}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-7, 0], -7, 是, 是)","explanation_zh":"結構基礎核對=([-7, 0], -7, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223081,"parameters":{"value":[-7,0],"real_candidate":-7,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-7,\"value\":[-7,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0082","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-6,0],\"real_candidate\":-5}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-6, 0], -5, 是, 否)","explanation_zh":"結構基礎核對=([-6, 0], -5, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223082,"parameters":{"value":[-6,0],"real_candidate":-5,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-5,\"value\":[-6,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0083","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-5,0],\"real_candidate\":-5}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-5, 0], -5, 是, 是)","explanation_zh":"結構基礎核對=([-5, 0], -5, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223083,"parameters":{"value":[-5,0],"real_candidate":-5,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-5,\"value\":[-5,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0084","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-4,1],\"real_candidate\":-4}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-4, 1], -4, 否, 否)","explanation_zh":"結構基礎核對=([-4, 1], -4, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223084,"parameters":{"value":[-4,1],"real_candidate":-4,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-4,\"value\":[-4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0085","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-3,0],\"real_candidate\":-2}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-3, 0], -2, 是, 否)","explanation_zh":"結構基礎核對=([-3, 0], -2, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223085,"parameters":{"value":[-3,0],"real_candidate":-2,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-2,\"value\":[-3,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0086","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-2,0],\"real_candidate\":-2}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-2, 0], -2, 是, 是)","explanation_zh":"結構基礎核對=([-2, 0], -2, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223086,"parameters":{"value":[-2,0],"real_candidate":-2,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-2,\"value\":[-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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0087","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[-1,0],\"real_candidate\":-1}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([-1, 0], -1, 是, 是)","explanation_zh":"結構基礎核對=([-1, 0], -1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223087,"parameters":{"value":[-1,0],"real_candidate":-1,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":-1,\"value\":[-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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0088","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[0,1],\"real_candidate\":1}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 1, 否, 否)","explanation_zh":"結構基礎核對=([0, 1], 1, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223088,"parameters":{"value":[0,1],"real_candidate":1,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":1,\"value\":[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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0089","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[1,0],\"real_candidate\":1}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([1, 0], 1, 是, 是)","explanation_zh":"結構基礎核對=([1, 0], 1, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223089,"parameters":{"value":[1,0],"real_candidate":1,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":1,\"value\":[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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0090","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[2,0],\"real_candidate\":2}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([2, 0], 2, 是, 是)","explanation_zh":"結構基礎核對=([2, 0], 2, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223090,"parameters":{"value":[2,0],"real_candidate":2,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":2,\"value\":[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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0091","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[3,0],\"real_candidate\":4}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([3, 0], 4, 是, 否)","explanation_zh":"結構基礎核對=([3, 0], 4, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223091,"parameters":{"value":[3,0],"real_candidate":4,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":4,\"value\":[3,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0092","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[4,1],\"real_candidate\":4}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([4, 1], 4, 否, 否)","explanation_zh":"結構基礎核對=([4, 1], 4, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223092,"parameters":{"value":[4,1],"real_candidate":4,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":4,\"value\":[4,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0093","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[5,0],\"real_candidate\":5}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([5, 0], 5, 是, 是)","explanation_zh":"結構基礎核對=([5, 0], 5, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223093,"parameters":{"value":[5,0],"real_candidate":5,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":5,\"value\":[5,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0094","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[6,0],\"real_candidate\":7}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([6, 0], 7, 是, 否)","explanation_zh":"結構基礎核對=([6, 0], 7, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223094,"parameters":{"value":[6,0],"real_candidate":7,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":7,\"value\":[6,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0095","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[7,0],\"real_candidate\":7}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([7, 0], 7, 是, 是)","explanation_zh":"結構基礎核對=([7, 0], 7, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223095,"parameters":{"value":[7,0],"real_candidate":7,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":7,\"value\":[7,0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0096","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[8,1],\"real_candidate\":8}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([8, 1], 8, 否, 否)","explanation_zh":"結構基礎核對=([8, 1], 8, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223096,"parameters":{"value":[8,1],"real_candidate":8,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":8,\"value\":[8,1]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0097","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[9,0],\"real_candidate\":10}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([9, 0], 10, 是, 否)","explanation_zh":"結構基礎核對=([9, 0], 10, 是, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223097,"parameters":{"value":[9,0],"real_candidate":10,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":10,\"value\":[9,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0098","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[10,0],\"real_candidate\":10}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([10, 0], 10, 是, 是)","explanation_zh":"結構基礎核對=([10, 0], 10, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223098,"parameters":{"value":[10,0],"real_candidate":10,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":10,\"value\":[10,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0099","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[11,0],\"real_candidate\":11}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([11, 0], 11, 是, 是)","explanation_zh":"結構基礎核對=([11, 0], 11, 是, 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223099,"parameters":{"value":[11,0],"real_candidate":11,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":11,\"value\":[11,0]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r03-complex-number-0100","batch_id":"batch-20261013-advance-20261022-r03-complex-number-foundations","language":"zh-Hant","source_mko_ids":["mko-complex-number"],"title_zh":"複數有序對運算","stem_zh":"複數以整數有序對表示。操作=complex-real-embedding-audit；資料={\"value\":[12,1],\"real_candidate\":13}。請依 [value,real_candidate,is_real_embedding,matches] 欄序回答。","answer":{"kind":"expression","value":"([12, 1], 13, 否, 否)","explanation_zh":"結構基礎核對=([12, 1], 13, 否, 否)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；有序對運算依i平方等於-1；不由複平面外觀補值。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["複數有序對運算"]},"variant":{"family_id":"qf-str22-complex-real-embedding-audit","seed":202610223100,"parameters":{"value":[12,1],"real_candidate":13,"domain":"Integer_pair_complex_arithmetic","operation":"complex-real-embedding-audit","semantic_template":"qf-str22-complex-real-embedding-audit/{\"real_candidate\":13,\"value\":[12,1]}"}},"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、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}