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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0004","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-period-update；資料={\"balance\":[71,4],\"rate\":[1,20]}。請依 [balance,rate,accumulation,next] 欄序回答。","answer":{"kind":"expression","value":"(71/4, 1/20, 21/20, 1491/80)","explanation_zh":"應用基礎核對=(71/4, 1/20, 21/20, 1491/80)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-period-update","seed":202610207004,"parameters":{"balance":[71,4],"rate":[1,20],"domain":"Exact_fixed_period_compound_model","operation":"interest-period-update","semantic_template":"qf-app20-interest-period-update/{\"balance\":[71,4],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0013","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-period-update；資料={\"balance\":[134,1],\"rate\":[0,20]}。請依 [balance,rate,accumulation,next] 欄序回答。","answer":{"kind":"expression","value":"(134, 0, 1, 134)","explanation_zh":"應用基礎核對=(134, 0, 1, 134)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-period-update","seed":202610207013,"parameters":{"balance":[134,1],"rate":[0,20],"domain":"Exact_fixed_period_compound_model","operation":"interest-period-update","semantic_template":"qf-app20-interest-period-update/{\"balance\":[134,1],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0014","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-period-update；資料={\"balance\":[141,2],\"rate\":[1,20]}。請依 [balance,rate,accumulation,next] 欄序回答。","answer":{"kind":"expression","value":"(141/2, 1/20, 21/20, 2961/40)","explanation_zh":"應用基礎核對=(141/2, 1/20, 21/20, 2961/40)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-period-update","seed":202610207014,"parameters":{"balance":[141,2],"rate":[1,20],"domain":"Exact_fixed_period_compound_model","operation":"interest-period-update","semantic_template":"qf-app20-interest-period-update/{\"balance\":[141,2],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0021","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-period-update；資料={\"balance\":[190,1],\"rate\":[-2,20]}。請依 [balance,rate,accumulation,next] 欄序回答。","answer":{"kind":"expression","value":"(190, -1/10, 9/10, 171)","explanation_zh":"應用基礎核對=(190, -1/10, 9/10, 171)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-period-update","seed":202610207021,"parameters":{"balance":[190,1],"rate":[-2,20],"domain":"Exact_fixed_period_compound_model","operation":"interest-period-update","semantic_template":"qf-app20-interest-period-update/{\"balance\":[190,1],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0022","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-period-update；資料={\"balance\":[197,2],\"rate\":[-1,20]}。請依 [balance,rate,accumulation,next] 欄序回答。","answer":{"kind":"expression","value":"(197/2, -1/20, 19/20, 3743/40)","explanation_zh":"應用基礎核對=(197/2, -1/20, 19/20, 3743/40)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-period-update","seed":202610207022,"parameters":{"balance":[197,2],"rate":[-1,20],"domain":"Exact_fixed_period_compound_model","operation":"interest-period-update","semantic_template":"qf-app20-interest-period-update/{\"balance\":[197,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0023","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-period-update；資料={\"balance\":[204,3],\"rate\":[0,20]}。請依 [balance,rate,accumulation,next] 欄序回答。","answer":{"kind":"expression","value":"(68, 0, 1, 68)","explanation_zh":"應用基礎核對=(68, 0, 1, 68)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-period-update","seed":202610207023,"parameters":{"balance":[204,3],"rate":[0,20],"domain":"Exact_fixed_period_compound_model","operation":"interest-period-update","semantic_template":"qf-app20-interest-period-update/{\"balance\":[204,3],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0024","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-period-update；資料={\"balance\":[211,4],\"rate\":[1,20]}。請依 [balance,rate,accumulation,next] 欄序回答。","answer":{"kind":"expression","value":"(211/4, 1/20, 21/20, 4431/80)","explanation_zh":"應用基礎核對=(211/4, 1/20, 21/20, 4431/80)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-period-update","seed":202610207024,"parameters":{"balance":[211,4],"rate":[1,20],"domain":"Exact_fixed_period_compound_model","operation":"interest-period-update","semantic_template":"qf-app20-interest-period-update/{\"balance\":[211,4],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0025","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-period-update；資料={\"balance\":[218,1],\"rate\":[2,20]}。請依 [balance,rate,accumulation,next] 欄序回答。","answer":{"kind":"expression","value":"(218, 1/10, 11/10, 1199/5)","explanation_zh":"應用基礎核對=(218, 1/10, 11/10, 1199/5)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-period-update","seed":202610207025,"parameters":{"balance":[218,1],"rate":[2,20],"domain":"Exact_fixed_period_compound_model","operation":"interest-period-update","semantic_template":"qf-app20-interest-period-update/{\"balance\":[218,1],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0026","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[100,1],\"rate\":[-2,20],\"periods\":0}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(100, -1/10, 9/10, 0, 100)","explanation_zh":"應用基礎核對=(100, -1/10, 9/10, 0, 100)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207026,"parameters":{"principal":[100,1],"rate":[-2,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[100,1],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0027","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[105,2],\"rate\":[-1,20],\"periods\":1}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(105/2, -1/20, 19/20, 1, 399/8)","explanation_zh":"應用基礎核對=(105/2, -1/20, 19/20, 1, 399/8)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207027,"parameters":{"principal":[105,2],"rate":[-1,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[105,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0028","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[110,3],\"rate\":[0,20],\"periods\":2}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(110/3, 0, 1, 2, 110/3)","explanation_zh":"應用基礎核對=(110/3, 0, 1, 2, 110/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207028,"parameters":{"principal":[110,3],"rate":[0,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[110,3],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0029","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[115,4],\"rate\":[1,20],\"periods\":0}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(115/4, 1/20, 21/20, 0, 115/4)","explanation_zh":"應用基礎核對=(115/4, 1/20, 21/20, 0, 115/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207029,"parameters":{"principal":[115,4],"rate":[1,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[115,4],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0030","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[120,1],\"rate\":[2,20],\"periods\":1}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(120, 1/10, 11/10, 1, 132)","explanation_zh":"應用基礎核對=(120, 1/10, 11/10, 1, 132)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207030,"parameters":{"principal":[120,1],"rate":[2,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[120,1],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0031","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[125,2],\"rate\":[-2,20],\"periods\":2}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(125/2, -1/10, 9/10, 2, 405/8)","explanation_zh":"應用基礎核對=(125/2, -1/10, 9/10, 2, 405/8)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207031,"parameters":{"principal":[125,2],"rate":[-2,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[125,2],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0032","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[130,3],\"rate\":[-1,20],\"periods\":0}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(130/3, -1/20, 19/20, 0, 130/3)","explanation_zh":"應用基礎核對=(130/3, -1/20, 19/20, 0, 130/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207032,"parameters":{"principal":[130,3],"rate":[-1,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[130,3],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0033","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[135,4],\"rate\":[0,20],\"periods\":1}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(135/4, 0, 1, 1, 135/4)","explanation_zh":"應用基礎核對=(135/4, 0, 1, 1, 135/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207033,"parameters":{"principal":[135,4],"rate":[0,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[135,4],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0034","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[140,1],\"rate\":[1,20],\"periods\":2}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(140, 1/20, 21/20, 2, 3087/20)","explanation_zh":"應用基礎核對=(140, 1/20, 21/20, 2, 3087/20)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207034,"parameters":{"principal":[140,1],"rate":[1,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[140,1],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0035","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[145,2],\"rate\":[2,20],\"periods\":0}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(145/2, 1/10, 11/10, 0, 145/2)","explanation_zh":"應用基礎核對=(145/2, 1/10, 11/10, 0, 145/2)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207035,"parameters":{"principal":[145,2],"rate":[2,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[145,2],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0036","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[150,3],\"rate\":[-2,20],\"periods\":1}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(50, -1/10, 9/10, 1, 45)","explanation_zh":"應用基礎核對=(50, -1/10, 9/10, 1, 45)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207036,"parameters":{"principal":[150,3],"rate":[-2,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[150,3],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0037","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[155,4],\"rate\":[-1,20],\"periods\":2}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(155/4, -1/20, 19/20, 2, 11191/320)","explanation_zh":"應用基礎核對=(155/4, -1/20, 19/20, 2, 11191/320)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207037,"parameters":{"principal":[155,4],"rate":[-1,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[155,4],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0038","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[160,1],\"rate\":[0,20],\"periods\":0}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(160, 0, 1, 0, 160)","explanation_zh":"應用基礎核對=(160, 0, 1, 0, 160)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207038,"parameters":{"principal":[160,1],"rate":[0,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[160,1],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0039","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[165,2],\"rate\":[1,20],\"periods\":1}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(165/2, 1/20, 21/20, 1, 693/8)","explanation_zh":"應用基礎核對=(165/2, 1/20, 21/20, 1, 693/8)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207039,"parameters":{"principal":[165,2],"rate":[1,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[165,2],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0040","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[170,3],\"rate\":[2,20],\"periods\":2}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(170/3, 1/10, 11/10, 2, 2057/30)","explanation_zh":"應用基礎核對=(170/3, 1/10, 11/10, 2, 2057/30)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207040,"parameters":{"principal":[170,3],"rate":[2,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[170,3],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0041","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[175,4],\"rate\":[-2,20],\"periods\":0}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(175/4, -1/10, 9/10, 0, 175/4)","explanation_zh":"應用基礎核對=(175/4, -1/10, 9/10, 0, 175/4)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207041,"parameters":{"principal":[175,4],"rate":[-2,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[175,4],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0042","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[180,1],\"rate\":[-1,20],\"periods\":1}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(180, -1/20, 19/20, 1, 171)","explanation_zh":"應用基礎核對=(180, -1/20, 19/20, 1, 171)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207042,"parameters":{"principal":[180,1],"rate":[-1,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[180,1],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0043","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[185,2],\"rate\":[0,20],\"periods\":2}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(185/2, 0, 1, 2, 185/2)","explanation_zh":"應用基礎核對=(185/2, 0, 1, 2, 185/2)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207043,"parameters":{"principal":[185,2],"rate":[0,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[185,2],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0044","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[190,3],\"rate\":[1,20],\"periods\":0}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(190/3, 1/20, 21/20, 0, 190/3)","explanation_zh":"應用基礎核對=(190/3, 1/20, 21/20, 0, 190/3)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207044,"parameters":{"principal":[190,3],"rate":[1,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[190,3],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0045","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[195,4],\"rate\":[2,20],\"periods\":1}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(195/4, 1/10, 11/10, 1, 429/8)","explanation_zh":"應用基礎核對=(195/4, 1/10, 11/10, 1, 429/8)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207045,"parameters":{"principal":[195,4],"rate":[2,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[195,4],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0046","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[200,1],\"rate\":[-2,20],\"periods\":2}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(200, -1/10, 9/10, 2, 162)","explanation_zh":"應用基礎核對=(200, -1/10, 9/10, 2, 162)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207046,"parameters":{"principal":[200,1],"rate":[-2,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[200,1],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0047","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[205,2],\"rate\":[-1,20],\"periods\":0}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(205/2, -1/20, 19/20, 0, 205/2)","explanation_zh":"應用基礎核對=(205/2, -1/20, 19/20, 0, 205/2)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207047,"parameters":{"principal":[205,2],"rate":[-1,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[205,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0048","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[210,3],\"rate\":[0,20],\"periods\":1}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(70, 0, 1, 1, 70)","explanation_zh":"應用基礎核對=(70, 0, 1, 1, 70)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207048,"parameters":{"principal":[210,3],"rate":[0,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":1,\"principal\":[210,3],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0049","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[215,4],\"rate\":[1,20],\"periods\":2}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(215/4, 1/20, 21/20, 2, 18963/320)","explanation_zh":"應用基礎核對=(215/4, 1/20, 21/20, 2, 18963/320)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207049,"parameters":{"principal":[215,4],"rate":[1,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":2,\"principal\":[215,4],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0050","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-future-value；資料={\"principal\":[220,1],\"rate\":[2,20],\"periods\":0}。請依 [principal,rate,accumulation,periods,future] 欄序回答。","answer":{"kind":"expression","value":"(220, 1/10, 11/10, 0, 220)","explanation_zh":"應用基礎核對=(220, 1/10, 11/10, 0, 220)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-future-value","seed":202610207050,"parameters":{"principal":[220,1],"rate":[2,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-future-value","semantic_template":"qf-app20-interest-future-value/{\"periods\":0,\"principal\":[220,1],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0051","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[100,1],\"rate\":[-1,10],\"periods\":0,\"candidate\":[101,1]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(100, -1/10, 0, 100, 101, 否)","explanation_zh":"應用基礎核對=(100, -1/10, 0, 100, 101, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207051,"parameters":{"principal":[100,1],"rate":[-1,10],"periods":0,"candidate":[101,1],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[101,1],\"periods\":0,\"principal\":[100,1],\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0052","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[105,2],\"rate\":[-1,20],\"periods\":1,\"candidate\":[399,8]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(105/2, -1/20, 1, 399/8, 399/8, 是)","explanation_zh":"應用基礎核對=(105/2, -1/20, 1, 399/8, 399/8, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207052,"parameters":{"principal":[105,2],"rate":[-1,20],"periods":1,"candidate":[399,8],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[399,8],\"periods\":1,\"principal\":[105,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0053","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[110,3],\"rate\":[0,1],\"periods\":2,\"candidate\":[110,3]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(110/3, 0, 2, 110/3, 110/3, 是)","explanation_zh":"應用基礎核對=(110/3, 0, 2, 110/3, 110/3, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207053,"parameters":{"principal":[110,3],"rate":[0,1],"periods":2,"candidate":[110,3],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[110,3],\"periods\":2,\"principal\":[110,3],\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0054","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[115,4],\"rate\":[1,20],\"periods\":0,\"candidate\":[116,4]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(115/4, 1/20, 0, 115/4, 29, 否)","explanation_zh":"應用基礎核對=(115/4, 1/20, 0, 115/4, 29, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207054,"parameters":{"principal":[115,4],"rate":[1,20],"periods":0,"candidate":[116,4],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[116,4],\"periods\":0,\"principal\":[115,4],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0055","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[120,1],\"rate\":[1,10],\"periods\":1,\"candidate\":[132,1]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(120, 1/10, 1, 132, 132, 是)","explanation_zh":"應用基礎核對=(120, 1/10, 1, 132, 132, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207055,"parameters":{"principal":[120,1],"rate":[1,10],"periods":1,"candidate":[132,1],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[132,1],\"periods\":1,\"principal\":[120,1],\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0056","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[125,2],\"rate\":[-1,10],\"periods\":2,\"candidate\":[405,8]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(125/2, -1/10, 2, 405/8, 405/8, 是)","explanation_zh":"應用基礎核對=(125/2, -1/10, 2, 405/8, 405/8, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207056,"parameters":{"principal":[125,2],"rate":[-1,10],"periods":2,"candidate":[405,8],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[405,8],\"periods\":2,\"principal\":[125,2],\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0057","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[130,3],\"rate\":[-1,20],\"periods\":0,\"candidate\":[131,3]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(130/3, -1/20, 0, 130/3, 131/3, 否)","explanation_zh":"應用基礎核對=(130/3, -1/20, 0, 130/3, 131/3, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207057,"parameters":{"principal":[130,3],"rate":[-1,20],"periods":0,"candidate":[131,3],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[131,3],\"periods\":0,\"principal\":[130,3],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0058","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[135,4],\"rate\":[0,1],\"periods\":1,\"candidate\":[135,4]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(135/4, 0, 1, 135/4, 135/4, 是)","explanation_zh":"應用基礎核對=(135/4, 0, 1, 135/4, 135/4, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207058,"parameters":{"principal":[135,4],"rate":[0,1],"periods":1,"candidate":[135,4],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[135,4],\"periods\":1,\"principal\":[135,4],\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0059","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[140,1],\"rate\":[1,20],\"periods\":2,\"candidate\":[3087,20]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(140, 1/20, 2, 3087/20, 3087/20, 是)","explanation_zh":"應用基礎核對=(140, 1/20, 2, 3087/20, 3087/20, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207059,"parameters":{"principal":[140,1],"rate":[1,20],"periods":2,"candidate":[3087,20],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[3087,20],\"periods\":2,\"principal\":[140,1],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0060","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[145,2],\"rate\":[1,10],\"periods\":0,\"candidate\":[146,2]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(145/2, 1/10, 0, 145/2, 73, 否)","explanation_zh":"應用基礎核對=(145/2, 1/10, 0, 145/2, 73, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207060,"parameters":{"principal":[145,2],"rate":[1,10],"periods":0,"candidate":[146,2],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[146,2],\"periods\":0,\"principal\":[145,2],\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0061","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[50,1],\"rate\":[-1,10],\"periods\":1,\"candidate\":[45,1]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(50, -1/10, 1, 45, 45, 是)","explanation_zh":"應用基礎核對=(50, -1/10, 1, 45, 45, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207061,"parameters":{"principal":[50,1],"rate":[-1,10],"periods":1,"candidate":[45,1],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[45,1],\"periods\":1,\"principal\":[50,1],\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0062","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[155,4],\"rate\":[-1,20],\"periods\":2,\"candidate\":[11191,320]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(155/4, -1/20, 2, 11191/320, 11191/320, 是)","explanation_zh":"應用基礎核對=(155/4, -1/20, 2, 11191/320, 11191/320, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207062,"parameters":{"principal":[155,4],"rate":[-1,20],"periods":2,"candidate":[11191,320],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[11191,320],\"periods\":2,\"principal\":[155,4],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0063","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[160,1],\"rate\":[0,1],\"periods\":0,\"candidate\":[161,1]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(160, 0, 0, 160, 161, 否)","explanation_zh":"應用基礎核對=(160, 0, 0, 160, 161, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207063,"parameters":{"principal":[160,1],"rate":[0,1],"periods":0,"candidate":[161,1],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[161,1],\"periods\":0,\"principal\":[160,1],\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0064","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[165,2],\"rate\":[1,20],\"periods\":1,\"candidate\":[693,8]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(165/2, 1/20, 1, 693/8, 693/8, 是)","explanation_zh":"應用基礎核對=(165/2, 1/20, 1, 693/8, 693/8, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207064,"parameters":{"principal":[165,2],"rate":[1,20],"periods":1,"candidate":[693,8],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[693,8],\"periods\":1,\"principal\":[165,2],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0065","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[170,3],\"rate\":[1,10],\"periods\":2,\"candidate\":[2057,30]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(170/3, 1/10, 2, 2057/30, 2057/30, 是)","explanation_zh":"應用基礎核對=(170/3, 1/10, 2, 2057/30, 2057/30, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207065,"parameters":{"principal":[170,3],"rate":[1,10],"periods":2,"candidate":[2057,30],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[2057,30],\"periods\":2,\"principal\":[170,3],\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0066","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[175,4],\"rate\":[-1,10],\"periods\":0,\"candidate\":[176,4]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(175/4, -1/10, 0, 175/4, 44, 否)","explanation_zh":"應用基礎核對=(175/4, -1/10, 0, 175/4, 44, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207066,"parameters":{"principal":[175,4],"rate":[-1,10],"periods":0,"candidate":[176,4],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[176,4],\"periods\":0,\"principal\":[175,4],\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0067","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[180,1],\"rate\":[-1,20],\"periods\":1,\"candidate\":[171,1]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(180, -1/20, 1, 171, 171, 是)","explanation_zh":"應用基礎核對=(180, -1/20, 1, 171, 171, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207067,"parameters":{"principal":[180,1],"rate":[-1,20],"periods":1,"candidate":[171,1],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[171,1],\"periods\":1,\"principal\":[180,1],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0068","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[185,2],\"rate\":[0,1],\"periods\":2,\"candidate\":[185,2]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(185/2, 0, 2, 185/2, 185/2, 是)","explanation_zh":"應用基礎核對=(185/2, 0, 2, 185/2, 185/2, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207068,"parameters":{"principal":[185,2],"rate":[0,1],"periods":2,"candidate":[185,2],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[185,2],\"periods\":2,\"principal\":[185,2],\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0069","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[190,3],\"rate\":[1,20],\"periods\":0,\"candidate\":[191,3]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(190/3, 1/20, 0, 190/3, 191/3, 否)","explanation_zh":"應用基礎核對=(190/3, 1/20, 0, 190/3, 191/3, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207069,"parameters":{"principal":[190,3],"rate":[1,20],"periods":0,"candidate":[191,3],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[191,3],\"periods\":0,\"principal\":[190,3],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0070","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[195,4],\"rate\":[1,10],\"periods\":1,\"candidate\":[429,8]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(195/4, 1/10, 1, 429/8, 429/8, 是)","explanation_zh":"應用基礎核對=(195/4, 1/10, 1, 429/8, 429/8, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207070,"parameters":{"principal":[195,4],"rate":[1,10],"periods":1,"candidate":[429,8],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[429,8],\"periods\":1,\"principal\":[195,4],\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0071","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[200,1],\"rate\":[-1,10],\"periods\":2,\"candidate\":[162,1]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(200, -1/10, 2, 162, 162, 是)","explanation_zh":"應用基礎核對=(200, -1/10, 2, 162, 162, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207071,"parameters":{"principal":[200,1],"rate":[-1,10],"periods":2,"candidate":[162,1],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[162,1],\"periods\":2,\"principal\":[200,1],\"rate\":[-1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0072","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[205,2],\"rate\":[-1,20],\"periods\":0,\"candidate\":[206,2]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(205/2, -1/20, 0, 205/2, 103, 否)","explanation_zh":"應用基礎核對=(205/2, -1/20, 0, 205/2, 103, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207072,"parameters":{"principal":[205,2],"rate":[-1,20],"periods":0,"candidate":[206,2],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[206,2],\"periods\":0,\"principal\":[205,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0073","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[70,1],\"rate\":[0,1],\"periods\":1,\"candidate\":[70,1]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(70, 0, 1, 70, 70, 是)","explanation_zh":"應用基礎核對=(70, 0, 1, 70, 70, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207073,"parameters":{"principal":[70,1],"rate":[0,1],"periods":1,"candidate":[70,1],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[70,1],\"periods\":1,\"principal\":[70,1],\"rate\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0074","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[215,4],\"rate\":[1,20],\"periods\":2,\"candidate\":[18963,320]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(215/4, 1/20, 2, 18963/320, 18963/320, 是)","explanation_zh":"應用基礎核對=(215/4, 1/20, 2, 18963/320, 18963/320, 是)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207074,"parameters":{"principal":[215,4],"rate":[1,20],"periods":2,"candidate":[18963,320],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[18963,320],\"periods\":2,\"principal\":[215,4],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0075","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-recurrence-power-audit；資料={\"principal\":[220,1],\"rate\":[1,10],\"periods\":0,\"candidate\":[221,1]}。請依 [principal,rate,periods,future,candidate,matches] 欄序回答。","answer":{"kind":"expression","value":"(220, 1/10, 0, 220, 221, 否)","explanation_zh":"應用基礎核對=(220, 1/10, 0, 220, 221, 否)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-recurrence-power-audit","seed":202610207075,"parameters":{"principal":[220,1],"rate":[1,10],"periods":0,"candidate":[221,1],"domain":"Exact_fixed_period_compound_model","operation":"interest-recurrence-power-audit","semantic_template":"qf-app20-interest-recurrence-power-audit/{\"candidate\":[221,1],\"periods\":0,\"principal\":[220,1],\"rate\":[1,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0076","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[100,1],\"rate\":[-2,20],\"periods\":0}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(100, -1/10, 0, 100, 0)","explanation_zh":"應用基礎核對=(100, -1/10, 0, 100, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207076,"parameters":{"principal":[100,1],"rate":[-2,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[100,1],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0077","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[105,2],\"rate\":[-1,20],\"periods\":1}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(105/2, -1/20, 1, 399/8, -21/8)","explanation_zh":"應用基礎核對=(105/2, -1/20, 1, 399/8, -21/8)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207077,"parameters":{"principal":[105,2],"rate":[-1,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[105,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0078","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[110,3],\"rate\":[0,20],\"periods\":2}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(110/3, 0, 2, 110/3, 0)","explanation_zh":"應用基礎核對=(110/3, 0, 2, 110/3, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207078,"parameters":{"principal":[110,3],"rate":[0,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[110,3],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0079","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[115,4],\"rate\":[1,20],\"periods\":0}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(115/4, 1/20, 0, 115/4, 0)","explanation_zh":"應用基礎核對=(115/4, 1/20, 0, 115/4, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207079,"parameters":{"principal":[115,4],"rate":[1,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[115,4],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0080","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[120,1],\"rate\":[2,20],\"periods\":1}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(120, 1/10, 1, 132, 12)","explanation_zh":"應用基礎核對=(120, 1/10, 1, 132, 12)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207080,"parameters":{"principal":[120,1],"rate":[2,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[120,1],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0081","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[125,2],\"rate\":[-2,20],\"periods\":2}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(125/2, -1/10, 2, 405/8, -95/8)","explanation_zh":"應用基礎核對=(125/2, -1/10, 2, 405/8, -95/8)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207081,"parameters":{"principal":[125,2],"rate":[-2,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[125,2],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0082","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[130,3],\"rate\":[-1,20],\"periods\":0}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(130/3, -1/20, 0, 130/3, 0)","explanation_zh":"應用基礎核對=(130/3, -1/20, 0, 130/3, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207082,"parameters":{"principal":[130,3],"rate":[-1,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[130,3],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0083","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[135,4],\"rate\":[0,20],\"periods\":1}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(135/4, 0, 1, 135/4, 0)","explanation_zh":"應用基礎核對=(135/4, 0, 1, 135/4, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207083,"parameters":{"principal":[135,4],"rate":[0,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[135,4],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0084","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[140,1],\"rate\":[1,20],\"periods\":2}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(140, 1/20, 2, 3087/20, 287/20)","explanation_zh":"應用基礎核對=(140, 1/20, 2, 3087/20, 287/20)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207084,"parameters":{"principal":[140,1],"rate":[1,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[140,1],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0085","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[145,2],\"rate\":[2,20],\"periods\":0}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(145/2, 1/10, 0, 145/2, 0)","explanation_zh":"應用基礎核對=(145/2, 1/10, 0, 145/2, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207085,"parameters":{"principal":[145,2],"rate":[2,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[145,2],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0086","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[150,3],\"rate\":[-2,20],\"periods\":1}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(50, -1/10, 1, 45, -5)","explanation_zh":"應用基礎核對=(50, -1/10, 1, 45, -5)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207086,"parameters":{"principal":[150,3],"rate":[-2,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[150,3],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0087","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[155,4],\"rate\":[-1,20],\"periods\":2}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(155/4, -1/20, 2, 11191/320, -1209/320)","explanation_zh":"應用基礎核對=(155/4, -1/20, 2, 11191/320, -1209/320)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207087,"parameters":{"principal":[155,4],"rate":[-1,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[155,4],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0088","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[160,1],\"rate\":[0,20],\"periods\":0}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(160, 0, 0, 160, 0)","explanation_zh":"應用基礎核對=(160, 0, 0, 160, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207088,"parameters":{"principal":[160,1],"rate":[0,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[160,1],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0089","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[165,2],\"rate\":[1,20],\"periods\":1}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(165/2, 1/20, 1, 693/8, 33/8)","explanation_zh":"應用基礎核對=(165/2, 1/20, 1, 693/8, 33/8)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207089,"parameters":{"principal":[165,2],"rate":[1,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[165,2],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0090","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[170,3],\"rate\":[2,20],\"periods\":2}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(170/3, 1/10, 2, 2057/30, 119/10)","explanation_zh":"應用基礎核對=(170/3, 1/10, 2, 2057/30, 119/10)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207090,"parameters":{"principal":[170,3],"rate":[2,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[170,3],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0091","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[175,4],\"rate\":[-2,20],\"periods\":0}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(175/4, -1/10, 0, 175/4, 0)","explanation_zh":"應用基礎核對=(175/4, -1/10, 0, 175/4, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207091,"parameters":{"principal":[175,4],"rate":[-2,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[175,4],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0092","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[180,1],\"rate\":[-1,20],\"periods\":1}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(180, -1/20, 1, 171, -9)","explanation_zh":"應用基礎核對=(180, -1/20, 1, 171, -9)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207092,"parameters":{"principal":[180,1],"rate":[-1,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[180,1],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0093","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[185,2],\"rate\":[0,20],\"periods\":2}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(185/2, 0, 2, 185/2, 0)","explanation_zh":"應用基礎核對=(185/2, 0, 2, 185/2, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207093,"parameters":{"principal":[185,2],"rate":[0,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[185,2],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0094","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[190,3],\"rate\":[1,20],\"periods\":0}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(190/3, 1/20, 0, 190/3, 0)","explanation_zh":"應用基礎核對=(190/3, 1/20, 0, 190/3, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207094,"parameters":{"principal":[190,3],"rate":[1,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[190,3],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0095","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[195,4],\"rate\":[2,20],\"periods\":1}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(195/4, 1/10, 1, 429/8, 39/8)","explanation_zh":"應用基礎核對=(195/4, 1/10, 1, 429/8, 39/8)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207095,"parameters":{"principal":[195,4],"rate":[2,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[195,4],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0096","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[200,1],\"rate\":[-2,20],\"periods\":2}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(200, -1/10, 2, 162, -38)","explanation_zh":"應用基礎核對=(200, -1/10, 2, 162, -38)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207096,"parameters":{"principal":[200,1],"rate":[-2,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[200,1],\"rate\":[-2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0097","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[205,2],\"rate\":[-1,20],\"periods\":0}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(205/2, -1/20, 0, 205/2, 0)","explanation_zh":"應用基礎核對=(205/2, -1/20, 0, 205/2, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207097,"parameters":{"principal":[205,2],"rate":[-1,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[205,2],\"rate\":[-1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0098","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[210,3],\"rate\":[0,20],\"periods\":1}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(70, 0, 1, 70, 0)","explanation_zh":"應用基礎核對=(70, 0, 1, 70, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207098,"parameters":{"principal":[210,3],"rate":[0,20],"periods":1,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":1,\"principal\":[210,3],\"rate\":[0,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0099","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[215,4],\"rate\":[1,20],\"periods\":2}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(215/4, 1/20, 2, 18963/320, 1763/320)","explanation_zh":"應用基礎核對=(215/4, 1/20, 2, 18963/320, 1763/320)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207099,"parameters":{"principal":[215,4],"rate":[1,20],"periods":2,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":2,\"principal\":[215,4],\"rate\":[1,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261020-r07-compound-interest-0100","batch_id":"batch-20261013-advance-20261020-r07-compound-interest-foundations","language":"zh-Hant","source_mko_ids":["mko-compound-interest"],"title_zh":"固定期複利模型","stem_zh":"固定每期利率且無現金流。操作=interest-interest-earned；資料={\"principal\":[220,1],\"rate\":[2,20],\"periods\":0}。請依 [principal,rate,periods,future,interest] 欄序回答。","answer":{"kind":"expression","value":"(220, 1/10, 0, 220, 0)","explanation_zh":"應用基礎核對=(220, 1/10, 0, 220, 0)；依完整明示資料重算；精確有限切片核對不是一般定理或經驗預測；期別與利率慣例已固定；不是投資建議或市場預測。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["固定期複利模型"]},"variant":{"family_id":"qf-app20-interest-interest-earned","seed":202610207100,"parameters":{"principal":[220,1],"rate":[2,20],"periods":0,"domain":"Exact_fixed_period_compound_model","operation":"interest-interest-earned","semantic_template":"qf-app20-interest-interest-earned/{\"periods\":0,\"principal\":[220,1],\"rate\":[2,20]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}