{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0001","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-0\",\"parsed\":false,\"elaborated\":false,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-0, [否, 否, 否, 否], 是, 解析失敗)","explanation_zh":"擴展基礎核對=(env-0, [否, 否, 否, 否], 是, 解析失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187001,"parameters":{"environment_id":"env-0","parsed":false,"elaborated":false,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":false,\"environment_id\":\"env-0\",\"parsed\":false,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0002","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-1\",\"parsed\":true,\"elaborated\":false,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-1, [是, 否, 否, 否], 是, elaboration失敗)","explanation_zh":"擴展基礎核對=(env-1, [是, 否, 否, 否], 是, elaboration失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187002,"parameters":{"environment_id":"env-1","parsed":true,"elaborated":false,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":false,\"environment_id\":\"env-1\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0003","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-2\",\"parsed\":true,\"elaborated\":true,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-2, [是, 是, 否, 否], 是, 型別未知)","explanation_zh":"擴展基礎核對=(env-2, [是, 是, 否, 否], 是, 型別未知)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187003,"parameters":{"environment_id":"env-2","parsed":true,"elaborated":true,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-2\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0004","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-3\",\"parsed\":true,\"elaborated\":true,\"type_known\":true,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-3, [是, 是, 是, 否], 是, 不是Prop)","explanation_zh":"擴展基礎核對=(env-3, [是, 是, 是, 否], 是, 不是Prop)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187004,"parameters":{"environment_id":"env-3","parsed":true,"elaborated":true,"type_known":true,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-3\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0005","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-4\",\"parsed\":true,\"elaborated\":true,\"type_known\":true,\"type_is_prop\":true}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-4, [是, 是, 是, 是], 是, 形式陳述)","explanation_zh":"擴展基礎核對=(env-4, [是, 是, 是, 是], 是, 形式陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187005,"parameters":{"environment_id":"env-4","parsed":true,"elaborated":true,"type_known":true,"type_is_prop":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-4\",\"parsed\":true,\"type_is_prop\":true,\"type_known\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0006","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-5\",\"parsed\":false,\"elaborated\":true,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-5, [否, 是, 否, 否], 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-5, [否, 是, 否, 否], 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187006,"parameters":{"environment_id":"env-5","parsed":false,"elaborated":true,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-5\",\"parsed\":false,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0007","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-6\",\"parsed\":false,\"elaborated\":false,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-6, [否, 否, 否, 否], 是, 解析失敗)","explanation_zh":"擴展基礎核對=(env-6, [否, 否, 否, 否], 是, 解析失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187007,"parameters":{"environment_id":"env-6","parsed":false,"elaborated":false,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":false,\"environment_id\":\"env-6\",\"parsed\":false,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0008","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-7\",\"parsed\":true,\"elaborated\":false,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-7, [是, 否, 否, 否], 是, elaboration失敗)","explanation_zh":"擴展基礎核對=(env-7, [是, 否, 否, 否], 是, elaboration失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187008,"parameters":{"environment_id":"env-7","parsed":true,"elaborated":false,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":false,\"environment_id\":\"env-7\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0009","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-8\",\"parsed\":true,\"elaborated\":true,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-8, [是, 是, 否, 否], 是, 型別未知)","explanation_zh":"擴展基礎核對=(env-8, [是, 是, 否, 否], 是, 型別未知)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187009,"parameters":{"environment_id":"env-8","parsed":true,"elaborated":true,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-8\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0010","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-9\",\"parsed\":true,\"elaborated\":true,\"type_known\":true,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-9, [是, 是, 是, 否], 是, 不是Prop)","explanation_zh":"擴展基礎核對=(env-9, [是, 是, 是, 否], 是, 不是Prop)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187010,"parameters":{"environment_id":"env-9","parsed":true,"elaborated":true,"type_known":true,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-9\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0011","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-10\",\"parsed\":true,\"elaborated\":true,\"type_known\":true,\"type_is_prop\":true}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-10, [是, 是, 是, 是], 是, 形式陳述)","explanation_zh":"擴展基礎核對=(env-10, [是, 是, 是, 是], 是, 形式陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187011,"parameters":{"environment_id":"env-10","parsed":true,"elaborated":true,"type_known":true,"type_is_prop":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-10\",\"parsed\":true,\"type_is_prop\":true,\"type_known\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0012","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-11\",\"parsed\":false,\"elaborated\":true,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-11, [否, 是, 否, 否], 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-11, [否, 是, 否, 否], 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187012,"parameters":{"environment_id":"env-11","parsed":false,"elaborated":true,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-11\",\"parsed\":false,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0013","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-12\",\"parsed\":false,\"elaborated\":false,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-12, [否, 否, 否, 否], 是, 解析失敗)","explanation_zh":"擴展基礎核對=(env-12, [否, 否, 否, 否], 是, 解析失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187013,"parameters":{"environment_id":"env-12","parsed":false,"elaborated":false,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":false,\"environment_id\":\"env-12\",\"parsed\":false,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0014","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-13\",\"parsed\":true,\"elaborated\":false,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-13, [是, 否, 否, 否], 是, elaboration失敗)","explanation_zh":"擴展基礎核對=(env-13, [是, 否, 否, 否], 是, elaboration失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187014,"parameters":{"environment_id":"env-13","parsed":true,"elaborated":false,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":false,\"environment_id\":\"env-13\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0015","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-14\",\"parsed\":true,\"elaborated\":true,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-14, [是, 是, 否, 否], 是, 型別未知)","explanation_zh":"擴展基礎核對=(env-14, [是, 是, 否, 否], 是, 型別未知)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187015,"parameters":{"environment_id":"env-14","parsed":true,"elaborated":true,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-14\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0016","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-15\",\"parsed\":true,\"elaborated\":true,\"type_known\":true,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-15, [是, 是, 是, 否], 是, 不是Prop)","explanation_zh":"擴展基礎核對=(env-15, [是, 是, 是, 否], 是, 不是Prop)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187016,"parameters":{"environment_id":"env-15","parsed":true,"elaborated":true,"type_known":true,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-15\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0017","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-16\",\"parsed\":true,\"elaborated\":true,\"type_known\":true,\"type_is_prop\":true}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-16, [是, 是, 是, 是], 是, 形式陳述)","explanation_zh":"擴展基礎核對=(env-16, [是, 是, 是, 是], 是, 形式陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187017,"parameters":{"environment_id":"env-16","parsed":true,"elaborated":true,"type_known":true,"type_is_prop":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-16\",\"parsed\":true,\"type_is_prop\":true,\"type_known\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0018","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-17\",\"parsed\":false,\"elaborated\":true,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-17, [否, 是, 否, 否], 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-17, [否, 是, 否, 否], 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187018,"parameters":{"environment_id":"env-17","parsed":false,"elaborated":true,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-17\",\"parsed\":false,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0019","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-18\",\"parsed\":false,\"elaborated\":false,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-18, [否, 否, 否, 否], 是, 解析失敗)","explanation_zh":"擴展基礎核對=(env-18, [否, 否, 否, 否], 是, 解析失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187019,"parameters":{"environment_id":"env-18","parsed":false,"elaborated":false,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":false,\"environment_id\":\"env-18\",\"parsed\":false,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0020","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-19\",\"parsed\":true,\"elaborated\":false,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-19, [是, 否, 否, 否], 是, elaboration失敗)","explanation_zh":"擴展基礎核對=(env-19, [是, 否, 否, 否], 是, elaboration失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187020,"parameters":{"environment_id":"env-19","parsed":true,"elaborated":false,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":false,\"environment_id\":\"env-19\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0021","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-20\",\"parsed\":true,\"elaborated\":true,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-20, [是, 是, 否, 否], 是, 型別未知)","explanation_zh":"擴展基礎核對=(env-20, [是, 是, 否, 否], 是, 型別未知)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187021,"parameters":{"environment_id":"env-20","parsed":true,"elaborated":true,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-20\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0022","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-21\",\"parsed\":true,\"elaborated\":true,\"type_known\":true,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-21, [是, 是, 是, 否], 是, 不是Prop)","explanation_zh":"擴展基礎核對=(env-21, [是, 是, 是, 否], 是, 不是Prop)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187022,"parameters":{"environment_id":"env-21","parsed":true,"elaborated":true,"type_known":true,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-21\",\"parsed\":true,\"type_is_prop\":false,\"type_known\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0023","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-22\",\"parsed\":true,\"elaborated\":true,\"type_known\":true,\"type_is_prop\":true}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-22, [是, 是, 是, 是], 是, 形式陳述)","explanation_zh":"擴展基礎核對=(env-22, [是, 是, 是, 是], 是, 形式陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187023,"parameters":{"environment_id":"env-22","parsed":true,"elaborated":true,"type_known":true,"type_is_prop":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-22\",\"parsed\":true,\"type_is_prop\":true,\"type_known\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0024","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-23\",\"parsed\":false,\"elaborated\":true,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-23, [否, 是, 否, 否], 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-23, [否, 是, 否, 否], 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187024,"parameters":{"environment_id":"env-23","parsed":false,"elaborated":true,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":true,\"environment_id\":\"env-23\",\"parsed\":false,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0025","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-pipeline-state；資料={\"environment_id\":\"env-24\",\"parsed\":false,\"elaborated\":false,\"type_known\":false,\"type_is_prop\":false}。請依 [environment,[parsed,elaborated,type_known,type_is_prop],coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-24, [否, 否, 否, 否], 是, 解析失敗)","explanation_zh":"擴展基礎核對=(env-24, [否, 否, 否, 否], 是, 解析失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-pipeline-state","seed":202610187025,"parameters":{"environment_id":"env-24","parsed":false,"elaborated":false,"type_known":false,"type_is_prop":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-pipeline-state","semantic_template":"qf-ext18-formal-pipeline-state/{\"elaborated\":false,\"environment_id\":\"env-24\",\"parsed\":false,\"type_is_prop\":false,\"type_known\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0026","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-0\",\"required_names\":[\"Nat\",\"x0\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-0, [Nat, x0], [h, Nat], [x0], 否)","explanation_zh":"擴展基礎核對=(env-0, [Nat, x0], [h, Nat], [x0], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187026,"parameters":{"environment_id":"env-0","required_names":["Nat","x0"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-0\",\"required_names\":[\"Nat\",\"x0\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0027","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-1\",\"required_names\":[\"Nat\",\"x1\"],\"available_names\":[\"Nat\",\"x1\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-1, [Nat, x1], [h, Nat, x1], [], 是)","explanation_zh":"擴展基礎核對=(env-1, [Nat, x1], [h, Nat, x1], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187027,"parameters":{"environment_id":"env-1","required_names":["Nat","x1"],"available_names":["Nat","x1","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x1\"],\"environment_id\":\"env-1\",\"required_names\":[\"Nat\",\"x1\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0028","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-2\",\"required_names\":[\"Nat\",\"x2\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-2, [Nat, x2], [h, Nat], [x2], 否)","explanation_zh":"擴展基礎核對=(env-2, [Nat, x2], [h, Nat], [x2], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187028,"parameters":{"environment_id":"env-2","required_names":["Nat","x2"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-2\",\"required_names\":[\"Nat\",\"x2\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0029","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-3\",\"required_names\":[\"Nat\",\"x3\"],\"available_names\":[\"Nat\",\"x3\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-3, [Nat, x3], [h, Nat, x3], [], 是)","explanation_zh":"擴展基礎核對=(env-3, [Nat, x3], [h, Nat, x3], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187029,"parameters":{"environment_id":"env-3","required_names":["Nat","x3"],"available_names":["Nat","x3","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x3\"],\"environment_id\":\"env-3\",\"required_names\":[\"Nat\",\"x3\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0030","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-4\",\"required_names\":[\"Nat\",\"x4\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-4, [Nat, x4], [h, Nat], [x4], 否)","explanation_zh":"擴展基礎核對=(env-4, [Nat, x4], [h, Nat], [x4], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187030,"parameters":{"environment_id":"env-4","required_names":["Nat","x4"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-4\",\"required_names\":[\"Nat\",\"x4\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0031","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-5\",\"required_names\":[\"Nat\",\"x5\"],\"available_names\":[\"Nat\",\"x5\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-5, [Nat, x5], [h, Nat, x5], [], 是)","explanation_zh":"擴展基礎核對=(env-5, [Nat, x5], [h, Nat, x5], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187031,"parameters":{"environment_id":"env-5","required_names":["Nat","x5"],"available_names":["Nat","x5","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x5\"],\"environment_id\":\"env-5\",\"required_names\":[\"Nat\",\"x5\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0032","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-6\",\"required_names\":[\"Nat\",\"x6\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-6, [Nat, x6], [h, Nat], [x6], 否)","explanation_zh":"擴展基礎核對=(env-6, [Nat, x6], [h, Nat], [x6], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187032,"parameters":{"environment_id":"env-6","required_names":["Nat","x6"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-6\",\"required_names\":[\"Nat\",\"x6\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0033","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-7\",\"required_names\":[\"Nat\",\"x7\"],\"available_names\":[\"Nat\",\"x7\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-7, [Nat, x7], [h, Nat, x7], [], 是)","explanation_zh":"擴展基礎核對=(env-7, [Nat, x7], [h, Nat, x7], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187033,"parameters":{"environment_id":"env-7","required_names":["Nat","x7"],"available_names":["Nat","x7","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x7\"],\"environment_id\":\"env-7\",\"required_names\":[\"Nat\",\"x7\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0034","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-8\",\"required_names\":[\"Nat\",\"x8\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-8, [Nat, x8], [h, Nat], [x8], 否)","explanation_zh":"擴展基礎核對=(env-8, [Nat, x8], [h, Nat], [x8], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187034,"parameters":{"environment_id":"env-8","required_names":["Nat","x8"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-8\",\"required_names\":[\"Nat\",\"x8\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0035","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-9\",\"required_names\":[\"Nat\",\"x9\"],\"available_names\":[\"Nat\",\"x9\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-9, [Nat, x9], [h, Nat, x9], [], 是)","explanation_zh":"擴展基礎核對=(env-9, [Nat, x9], [h, Nat, x9], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187035,"parameters":{"environment_id":"env-9","required_names":["Nat","x9"],"available_names":["Nat","x9","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x9\"],\"environment_id\":\"env-9\",\"required_names\":[\"Nat\",\"x9\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0036","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-10\",\"required_names\":[\"Nat\",\"x10\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-10, [Nat, x10], [h, Nat], [x10], 否)","explanation_zh":"擴展基礎核對=(env-10, [Nat, x10], [h, Nat], [x10], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187036,"parameters":{"environment_id":"env-10","required_names":["Nat","x10"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-10\",\"required_names\":[\"Nat\",\"x10\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0037","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-11\",\"required_names\":[\"Nat\",\"x11\"],\"available_names\":[\"Nat\",\"x11\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-11, [Nat, x11], [h, Nat, x11], [], 是)","explanation_zh":"擴展基礎核對=(env-11, [Nat, x11], [h, Nat, x11], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187037,"parameters":{"environment_id":"env-11","required_names":["Nat","x11"],"available_names":["Nat","x11","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x11\"],\"environment_id\":\"env-11\",\"required_names\":[\"Nat\",\"x11\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0038","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-12\",\"required_names\":[\"Nat\",\"x12\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-12, [Nat, x12], [h, Nat], [x12], 否)","explanation_zh":"擴展基礎核對=(env-12, [Nat, x12], [h, Nat], [x12], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187038,"parameters":{"environment_id":"env-12","required_names":["Nat","x12"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-12\",\"required_names\":[\"Nat\",\"x12\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0039","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-13\",\"required_names\":[\"Nat\",\"x13\"],\"available_names\":[\"Nat\",\"x13\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-13, [Nat, x13], [h, Nat, x13], [], 是)","explanation_zh":"擴展基礎核對=(env-13, [Nat, x13], [h, Nat, x13], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187039,"parameters":{"environment_id":"env-13","required_names":["Nat","x13"],"available_names":["Nat","x13","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x13\"],\"environment_id\":\"env-13\",\"required_names\":[\"Nat\",\"x13\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0040","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-14\",\"required_names\":[\"Nat\",\"x14\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-14, [Nat, x14], [h, Nat], [x14], 否)","explanation_zh":"擴展基礎核對=(env-14, [Nat, x14], [h, Nat], [x14], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187040,"parameters":{"environment_id":"env-14","required_names":["Nat","x14"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-14\",\"required_names\":[\"Nat\",\"x14\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0041","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-15\",\"required_names\":[\"Nat\",\"x15\"],\"available_names\":[\"Nat\",\"x15\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-15, [Nat, x15], [h, Nat, x15], [], 是)","explanation_zh":"擴展基礎核對=(env-15, [Nat, x15], [h, Nat, x15], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187041,"parameters":{"environment_id":"env-15","required_names":["Nat","x15"],"available_names":["Nat","x15","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x15\"],\"environment_id\":\"env-15\",\"required_names\":[\"Nat\",\"x15\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0042","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-16\",\"required_names\":[\"Nat\",\"x16\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-16, [Nat, x16], [h, Nat], [x16], 否)","explanation_zh":"擴展基礎核對=(env-16, [Nat, x16], [h, Nat], [x16], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187042,"parameters":{"environment_id":"env-16","required_names":["Nat","x16"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-16\",\"required_names\":[\"Nat\",\"x16\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0043","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-17\",\"required_names\":[\"Nat\",\"x17\"],\"available_names\":[\"Nat\",\"x17\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-17, [Nat, x17], [h, Nat, x17], [], 是)","explanation_zh":"擴展基礎核對=(env-17, [Nat, x17], [h, Nat, x17], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187043,"parameters":{"environment_id":"env-17","required_names":["Nat","x17"],"available_names":["Nat","x17","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x17\"],\"environment_id\":\"env-17\",\"required_names\":[\"Nat\",\"x17\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0044","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-18\",\"required_names\":[\"Nat\",\"x18\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-18, [Nat, x18], [h, Nat], [x18], 否)","explanation_zh":"擴展基礎核對=(env-18, [Nat, x18], [h, Nat], [x18], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187044,"parameters":{"environment_id":"env-18","required_names":["Nat","x18"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-18\",\"required_names\":[\"Nat\",\"x18\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0045","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-19\",\"required_names\":[\"Nat\",\"x19\"],\"available_names\":[\"Nat\",\"x19\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-19, [Nat, x19], [h, Nat, x19], [], 是)","explanation_zh":"擴展基礎核對=(env-19, [Nat, x19], [h, Nat, x19], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187045,"parameters":{"environment_id":"env-19","required_names":["Nat","x19"],"available_names":["Nat","x19","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x19\"],\"environment_id\":\"env-19\",\"required_names\":[\"Nat\",\"x19\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0046","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-20\",\"required_names\":[\"Nat\",\"x20\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-20, [Nat, x20], [h, Nat], [x20], 否)","explanation_zh":"擴展基礎核對=(env-20, [Nat, x20], [h, Nat], [x20], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187046,"parameters":{"environment_id":"env-20","required_names":["Nat","x20"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-20\",\"required_names\":[\"Nat\",\"x20\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0047","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-21\",\"required_names\":[\"Nat\",\"x21\"],\"available_names\":[\"Nat\",\"x21\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-21, [Nat, x21], [h, Nat, x21], [], 是)","explanation_zh":"擴展基礎核對=(env-21, [Nat, x21], [h, Nat, x21], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187047,"parameters":{"environment_id":"env-21","required_names":["Nat","x21"],"available_names":["Nat","x21","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x21\"],\"environment_id\":\"env-21\",\"required_names\":[\"Nat\",\"x21\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0048","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-22\",\"required_names\":[\"Nat\",\"x22\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-22, [Nat, x22], [h, Nat], [x22], 否)","explanation_zh":"擴展基礎核對=(env-22, [Nat, x22], [h, Nat], [x22], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187048,"parameters":{"environment_id":"env-22","required_names":["Nat","x22"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-22\",\"required_names\":[\"Nat\",\"x22\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0049","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-23\",\"required_names\":[\"Nat\",\"x23\"],\"available_names\":[\"Nat\",\"x23\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-23, [Nat, x23], [h, Nat, x23], [], 是)","explanation_zh":"擴展基礎核對=(env-23, [Nat, x23], [h, Nat, x23], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187049,"parameters":{"environment_id":"env-23","required_names":["Nat","x23"],"available_names":["Nat","x23","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\",\"x23\"],\"environment_id\":\"env-23\",\"required_names\":[\"Nat\",\"x23\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0050","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-context-inventory；資料={\"environment_id\":\"env-24\",\"required_names\":[\"Nat\",\"x24\"],\"available_names\":[\"Nat\",\"h\"]}。請依 [environment,required,available,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(env-24, [Nat, x24], [h, Nat], [x24], 否)","explanation_zh":"擴展基礎核對=(env-24, [Nat, x24], [h, Nat], [x24], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-context-inventory","seed":202610187050,"parameters":{"environment_id":"env-24","required_names":["Nat","x24"],"available_names":["Nat","h"],"domain":"Synthetic_formal_statement_receipt","operation":"formal-context-inventory","semantic_template":"qf-ext18-formal-context-inventory/{\"available_names\":[\"h\",\"Nat\"],\"environment_id\":\"env-24\",\"required_names\":[\"Nat\",\"x24\"]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0051","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-0\",\"statement_elaborated_prop\":false,\"proof_term_present\":false,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-0, 否, 否, 否, 是, 沒有形式陳述)","explanation_zh":"擴展基礎核對=(env-0, 否, 否, 否, 是, 沒有形式陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187051,"parameters":{"environment_id":"env-0","statement_elaborated_prop":false,"proof_term_present":false,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-0\",\"kernel_checked\":false,\"proof_term_present\":false,\"statement_elaborated_prop\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0052","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-1\",\"statement_elaborated_prop\":true,\"proof_term_present\":false,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-1, 是, 否, 否, 是, 只有陳述)","explanation_zh":"擴展基礎核對=(env-1, 是, 否, 否, 是, 只有陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187052,"parameters":{"environment_id":"env-1","statement_elaborated_prop":true,"proof_term_present":false,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-1\",\"kernel_checked\":false,\"proof_term_present\":false,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0053","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-2\",\"statement_elaborated_prop\":true,\"proof_term_present\":true,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-2, 是, 是, 否, 是, 未檢查證明候選)","explanation_zh":"擴展基礎核對=(env-2, 是, 是, 否, 是, 未檢查證明候選)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187053,"parameters":{"environment_id":"env-2","statement_elaborated_prop":true,"proof_term_present":true,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-2\",\"kernel_checked\":false,\"proof_term_present\":true,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0054","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-3\",\"statement_elaborated_prop\":true,\"proof_term_present\":true,\"kernel_checked\":true}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-3, 是, 是, 是, 是, 已有kernel receipt)","explanation_zh":"擴展基礎核對=(env-3, 是, 是, 是, 是, 已有kernel receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187054,"parameters":{"environment_id":"env-3","statement_elaborated_prop":true,"proof_term_present":true,"kernel_checked":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-3\",\"kernel_checked\":true,\"proof_term_present\":true,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0055","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-4\",\"statement_elaborated_prop\":false,\"proof_term_present\":true,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-4, 否, 是, 否, 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-4, 否, 是, 否, 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187055,"parameters":{"environment_id":"env-4","statement_elaborated_prop":false,"proof_term_present":true,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-4\",\"kernel_checked\":false,\"proof_term_present\":true,\"statement_elaborated_prop\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0056","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-5\",\"statement_elaborated_prop\":true,\"proof_term_present\":false,\"kernel_checked\":true}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-5, 是, 否, 是, 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-5, 是, 否, 是, 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187056,"parameters":{"environment_id":"env-5","statement_elaborated_prop":true,"proof_term_present":false,"kernel_checked":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-5\",\"kernel_checked\":true,\"proof_term_present\":false,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0057","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-6\",\"statement_elaborated_prop\":false,\"proof_term_present\":false,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-6, 否, 否, 否, 是, 沒有形式陳述)","explanation_zh":"擴展基礎核對=(env-6, 否, 否, 否, 是, 沒有形式陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187057,"parameters":{"environment_id":"env-6","statement_elaborated_prop":false,"proof_term_present":false,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-6\",\"kernel_checked\":false,\"proof_term_present\":false,\"statement_elaborated_prop\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0058","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-7\",\"statement_elaborated_prop\":true,\"proof_term_present\":false,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-7, 是, 否, 否, 是, 只有陳述)","explanation_zh":"擴展基礎核對=(env-7, 是, 否, 否, 是, 只有陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187058,"parameters":{"environment_id":"env-7","statement_elaborated_prop":true,"proof_term_present":false,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-7\",\"kernel_checked\":false,\"proof_term_present\":false,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0059","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-8\",\"statement_elaborated_prop\":true,\"proof_term_present\":true,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-8, 是, 是, 否, 是, 未檢查證明候選)","explanation_zh":"擴展基礎核對=(env-8, 是, 是, 否, 是, 未檢查證明候選)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187059,"parameters":{"environment_id":"env-8","statement_elaborated_prop":true,"proof_term_present":true,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-8\",\"kernel_checked\":false,\"proof_term_present\":true,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0060","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-9\",\"statement_elaborated_prop\":true,\"proof_term_present\":true,\"kernel_checked\":true}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-9, 是, 是, 是, 是, 已有kernel receipt)","explanation_zh":"擴展基礎核對=(env-9, 是, 是, 是, 是, 已有kernel receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187060,"parameters":{"environment_id":"env-9","statement_elaborated_prop":true,"proof_term_present":true,"kernel_checked":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-9\",\"kernel_checked\":true,\"proof_term_present\":true,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0061","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-10\",\"statement_elaborated_prop\":false,\"proof_term_present\":true,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-10, 否, 是, 否, 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-10, 否, 是, 否, 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187061,"parameters":{"environment_id":"env-10","statement_elaborated_prop":false,"proof_term_present":true,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-10\",\"kernel_checked\":false,\"proof_term_present\":true,\"statement_elaborated_prop\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0062","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-11\",\"statement_elaborated_prop\":true,\"proof_term_present\":false,\"kernel_checked\":true}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-11, 是, 否, 是, 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-11, 是, 否, 是, 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187062,"parameters":{"environment_id":"env-11","statement_elaborated_prop":true,"proof_term_present":false,"kernel_checked":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-11\",\"kernel_checked\":true,\"proof_term_present\":false,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0063","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-12\",\"statement_elaborated_prop\":false,\"proof_term_present\":false,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-12, 否, 否, 否, 是, 沒有形式陳述)","explanation_zh":"擴展基礎核對=(env-12, 否, 否, 否, 是, 沒有形式陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187063,"parameters":{"environment_id":"env-12","statement_elaborated_prop":false,"proof_term_present":false,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-12\",\"kernel_checked\":false,\"proof_term_present\":false,\"statement_elaborated_prop\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0064","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-13\",\"statement_elaborated_prop\":true,\"proof_term_present\":false,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-13, 是, 否, 否, 是, 只有陳述)","explanation_zh":"擴展基礎核對=(env-13, 是, 否, 否, 是, 只有陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187064,"parameters":{"environment_id":"env-13","statement_elaborated_prop":true,"proof_term_present":false,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-13\",\"kernel_checked\":false,\"proof_term_present\":false,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0065","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-14\",\"statement_elaborated_prop\":true,\"proof_term_present\":true,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-14, 是, 是, 否, 是, 未檢查證明候選)","explanation_zh":"擴展基礎核對=(env-14, 是, 是, 否, 是, 未檢查證明候選)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187065,"parameters":{"environment_id":"env-14","statement_elaborated_prop":true,"proof_term_present":true,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-14\",\"kernel_checked\":false,\"proof_term_present\":true,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0066","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-15\",\"statement_elaborated_prop\":true,\"proof_term_present\":true,\"kernel_checked\":true}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-15, 是, 是, 是, 是, 已有kernel receipt)","explanation_zh":"擴展基礎核對=(env-15, 是, 是, 是, 是, 已有kernel receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187066,"parameters":{"environment_id":"env-15","statement_elaborated_prop":true,"proof_term_present":true,"kernel_checked":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-15\",\"kernel_checked\":true,\"proof_term_present\":true,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0067","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-16\",\"statement_elaborated_prop\":false,\"proof_term_present\":true,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-16, 否, 是, 否, 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-16, 否, 是, 否, 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187067,"parameters":{"environment_id":"env-16","statement_elaborated_prop":false,"proof_term_present":true,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-16\",\"kernel_checked\":false,\"proof_term_present\":true,\"statement_elaborated_prop\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0068","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-17\",\"statement_elaborated_prop\":true,\"proof_term_present\":false,\"kernel_checked\":true}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-17, 是, 否, 是, 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-17, 是, 否, 是, 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187068,"parameters":{"environment_id":"env-17","statement_elaborated_prop":true,"proof_term_present":false,"kernel_checked":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-17\",\"kernel_checked\":true,\"proof_term_present\":false,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0069","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-18\",\"statement_elaborated_prop\":false,\"proof_term_present\":false,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-18, 否, 否, 否, 是, 沒有形式陳述)","explanation_zh":"擴展基礎核對=(env-18, 否, 否, 否, 是, 沒有形式陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187069,"parameters":{"environment_id":"env-18","statement_elaborated_prop":false,"proof_term_present":false,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-18\",\"kernel_checked\":false,\"proof_term_present\":false,\"statement_elaborated_prop\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0070","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-19\",\"statement_elaborated_prop\":true,\"proof_term_present\":false,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-19, 是, 否, 否, 是, 只有陳述)","explanation_zh":"擴展基礎核對=(env-19, 是, 否, 否, 是, 只有陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187070,"parameters":{"environment_id":"env-19","statement_elaborated_prop":true,"proof_term_present":false,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-19\",\"kernel_checked\":false,\"proof_term_present\":false,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0071","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-20\",\"statement_elaborated_prop\":true,\"proof_term_present\":true,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-20, 是, 是, 否, 是, 未檢查證明候選)","explanation_zh":"擴展基礎核對=(env-20, 是, 是, 否, 是, 未檢查證明候選)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187071,"parameters":{"environment_id":"env-20","statement_elaborated_prop":true,"proof_term_present":true,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-20\",\"kernel_checked\":false,\"proof_term_present\":true,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0072","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-21\",\"statement_elaborated_prop\":true,\"proof_term_present\":true,\"kernel_checked\":true}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-21, 是, 是, 是, 是, 已有kernel receipt)","explanation_zh":"擴展基礎核對=(env-21, 是, 是, 是, 是, 已有kernel receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187072,"parameters":{"environment_id":"env-21","statement_elaborated_prop":true,"proof_term_present":true,"kernel_checked":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-21\",\"kernel_checked\":true,\"proof_term_present\":true,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0073","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-22\",\"statement_elaborated_prop\":false,\"proof_term_present\":true,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-22, 否, 是, 否, 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-22, 否, 是, 否, 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187073,"parameters":{"environment_id":"env-22","statement_elaborated_prop":false,"proof_term_present":true,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-22\",\"kernel_checked\":false,\"proof_term_present\":true,\"statement_elaborated_prop\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0074","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-23\",\"statement_elaborated_prop\":true,\"proof_term_present\":false,\"kernel_checked\":true}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-23, 是, 否, 是, 否, 不一致receipt)","explanation_zh":"擴展基礎核對=(env-23, 是, 否, 是, 否, 不一致receipt)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187074,"parameters":{"environment_id":"env-23","statement_elaborated_prop":true,"proof_term_present":false,"kernel_checked":true,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-23\",\"kernel_checked\":true,\"proof_term_present\":false,\"statement_elaborated_prop\":true}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0075","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-statement-proof-separation；資料={\"environment_id\":\"env-24\",\"statement_elaborated_prop\":false,\"proof_term_present\":false,\"kernel_checked\":false}。請依 [environment,statement,proof,kernel,coherent,state] 的欄序回答。","answer":{"kind":"expression","value":"(env-24, 否, 否, 否, 是, 沒有形式陳述)","explanation_zh":"擴展基礎核對=(env-24, 否, 否, 否, 是, 沒有形式陳述)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-statement-proof-separation","seed":202610187075,"parameters":{"environment_id":"env-24","statement_elaborated_prop":false,"proof_term_present":false,"kernel_checked":false,"domain":"Synthetic_formal_statement_receipt","operation":"formal-statement-proof-separation","semantic_template":"qf-ext18-formal-statement-proof-separation/{\"environment_id\":\"env-24\",\"kernel_checked\":false,\"proof_term_present\":false,\"statement_elaborated_prop\":false}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0076","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"\",\"imports\":[],\"imports_declared\":false,\"environment_id\":\"\",\"context_id\":\"\",\"source_sha256\":\"bad\",\"core_type\":\"Type\",\"elaboration_status\":\"failed\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(缺, [], 否, 缺, 缺, 否, Type, failed, [lean_version, imports_declaration, environment_id, context_id, source_sha256, core_type_Prop, elaboration_success], 否)","explanation_zh":"擴展基礎核對=(缺, [], 否, 缺, 缺, 否, Type, failed, [lean_version, imports_declaration, environment_id, context_id, source_sha256, core_type_Prop, elaboration_success], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187076,"parameters":{"lean_version":"","imports":[],"imports_declared":false,"environment_id":"","context_id":"","source_sha256":"bad","core_type":"Type","elaboration_status":"failed","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"\",\"core_type\":\"Type\",\"elaboration_status\":\"failed\",\"environment_id\":\"\",\"imports\":[],\"imports_declared\":false,\"lean_version\":\"\",\"source_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0077","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.21.0\",\"imports\":[\"Mathlib\",\"Module1\"],\"imports_declared\":true,\"environment_id\":\"env-1\",\"context_id\":\"ctx-1\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000001\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.21.0, [Mathlib, Module1], 是, env-1, ctx-1, 是, Prop, success, [], 是)","explanation_zh":"擴展基礎核對=(4.21.0, [Mathlib, Module1], 是, env-1, ctx-1, 是, Prop, success, [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187077,"parameters":{"lean_version":"4.21.0","imports":["Mathlib","Module1"],"imports_declared":true,"environment_id":"env-1","context_id":"ctx-1","source_sha256":"0000000000000000000000000000000000000000000000000000000000000001","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-1\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-1\",\"imports\":[\"Mathlib\",\"Module1\"],\"imports_declared\":true,\"lean_version\":\"4.21.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000001\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0078","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.22.0\",\"imports\":[\"Mathlib\",\"Module2\"],\"imports_declared\":true,\"environment_id\":\"env-2\",\"context_id\":\"ctx-2\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.22.0, [Mathlib, Module2], 是, env-2, ctx-2, 是, Prop, success, [], 是)","explanation_zh":"擴展基礎核對=(4.22.0, [Mathlib, Module2], 是, env-2, ctx-2, 是, Prop, success, [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187078,"parameters":{"lean_version":"4.22.0","imports":["Mathlib","Module2"],"imports_declared":true,"environment_id":"env-2","context_id":"ctx-2","source_sha256":"0000000000000000000000000000000000000000000000000000000000000002","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-2\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-2\",\"imports\":[\"Mathlib\",\"Module2\"],\"imports_declared\":true,\"lean_version\":\"4.22.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000002\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0079","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.23.0\",\"imports\":[\"Mathlib\",\"Module3\"],\"imports_declared\":true,\"environment_id\":\"env-3\",\"context_id\":\"ctx-3\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000003\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.23.0, [Mathlib, Module3], 是, env-3, ctx-3, 是, Prop, success, [], 是)","explanation_zh":"擴展基礎核對=(4.23.0, [Mathlib, Module3], 是, env-3, ctx-3, 是, Prop, success, [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187079,"parameters":{"lean_version":"4.23.0","imports":["Mathlib","Module3"],"imports_declared":true,"environment_id":"env-3","context_id":"ctx-3","source_sha256":"0000000000000000000000000000000000000000000000000000000000000003","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-3\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-3\",\"imports\":[\"Mathlib\",\"Module3\"],\"imports_declared\":true,\"lean_version\":\"4.23.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000003\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0080","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.24.0\",\"imports\":[],\"imports_declared\":true,\"environment_id\":\"env-4\",\"context_id\":\"ctx-4\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000004\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.24.0, [], 是, env-4, ctx-4, 是, Prop, success, [], 是)","explanation_zh":"擴展基礎核對=(4.24.0, [], 是, env-4, ctx-4, 是, Prop, success, [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187080,"parameters":{"lean_version":"4.24.0","imports":[],"imports_declared":true,"environment_id":"env-4","context_id":"ctx-4","source_sha256":"0000000000000000000000000000000000000000000000000000000000000004","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-4\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-4\",\"imports\":[],\"imports_declared\":true,\"lean_version\":\"4.24.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000004\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0081","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"\",\"imports\":[\"Mathlib\",\"Module5\"],\"imports_declared\":true,\"environment_id\":\"env-5\",\"context_id\":\"ctx-5\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000005\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(缺, [Mathlib, Module5], 是, env-5, ctx-5, 是, Prop, success, [lean_version], 否)","explanation_zh":"擴展基礎核對=(缺, [Mathlib, Module5], 是, env-5, ctx-5, 是, Prop, success, [lean_version], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187081,"parameters":{"lean_version":"","imports":["Mathlib","Module5"],"imports_declared":true,"environment_id":"env-5","context_id":"ctx-5","source_sha256":"0000000000000000000000000000000000000000000000000000000000000005","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-5\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-5\",\"imports\":[\"Mathlib\",\"Module5\"],\"imports_declared\":true,\"lean_version\":\"\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000005\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0082","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.26.0\",\"imports\":[\"Mathlib\",\"Module6\"],\"imports_declared\":false,\"environment_id\":\"env-6\",\"context_id\":\"ctx-6\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000006\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.26.0, [Mathlib, Module6], 否, env-6, ctx-6, 是, Prop, success, [imports_declaration], 否)","explanation_zh":"擴展基礎核對=(4.26.0, [Mathlib, Module6], 否, env-6, ctx-6, 是, Prop, success, [imports_declaration], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187082,"parameters":{"lean_version":"4.26.0","imports":["Mathlib","Module6"],"imports_declared":false,"environment_id":"env-6","context_id":"ctx-6","source_sha256":"0000000000000000000000000000000000000000000000000000000000000006","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-6\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-6\",\"imports\":[\"Mathlib\",\"Module6\"],\"imports_declared\":false,\"lean_version\":\"4.26.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000006\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0083","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.27.0\",\"imports\":[\"Mathlib\",\"Module7\"],\"imports_declared\":true,\"environment_id\":\"\",\"context_id\":\"ctx-7\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000007\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.27.0, [Mathlib, Module7], 是, 缺, ctx-7, 是, Prop, success, [environment_id], 否)","explanation_zh":"擴展基礎核對=(4.27.0, [Mathlib, Module7], 是, 缺, ctx-7, 是, Prop, success, [environment_id], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187083,"parameters":{"lean_version":"4.27.0","imports":["Mathlib","Module7"],"imports_declared":true,"environment_id":"","context_id":"ctx-7","source_sha256":"0000000000000000000000000000000000000000000000000000000000000007","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-7\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"\",\"imports\":[\"Mathlib\",\"Module7\"],\"imports_declared\":true,\"lean_version\":\"4.27.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000007\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0084","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.28.0\",\"imports\":[],\"imports_declared\":true,\"environment_id\":\"env-8\",\"context_id\":\"\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000008\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.28.0, [], 是, env-8, 缺, 是, Prop, success, [context_id], 否)","explanation_zh":"擴展基礎核對=(4.28.0, [], 是, env-8, 缺, 是, Prop, success, [context_id], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187084,"parameters":{"lean_version":"4.28.0","imports":[],"imports_declared":true,"environment_id":"env-8","context_id":"","source_sha256":"0000000000000000000000000000000000000000000000000000000000000008","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-8\",\"imports\":[],\"imports_declared\":true,\"lean_version\":\"4.28.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000008\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0085","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.29.0\",\"imports\":[\"Mathlib\",\"Module9\"],\"imports_declared\":true,\"environment_id\":\"env-9\",\"context_id\":\"ctx-9\",\"source_sha256\":\"bad\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.29.0, [Mathlib, Module9], 是, env-9, ctx-9, 否, Prop, success, [source_sha256], 否)","explanation_zh":"擴展基礎核對=(4.29.0, [Mathlib, Module9], 是, env-9, ctx-9, 否, Prop, success, [source_sha256], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187085,"parameters":{"lean_version":"4.29.0","imports":["Mathlib","Module9"],"imports_declared":true,"environment_id":"env-9","context_id":"ctx-9","source_sha256":"bad","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-9\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-9\",\"imports\":[\"Mathlib\",\"Module9\"],\"imports_declared\":true,\"lean_version\":\"4.29.0\",\"source_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0086","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"\",\"imports\":[\"Mathlib\",\"Module10\"],\"imports_declared\":true,\"environment_id\":\"env-10\",\"context_id\":\"ctx-10\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\",\"core_type\":\"Type\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(缺, [Mathlib, Module10], 是, env-10, ctx-10, 是, Type, success, [lean_version, core_type_Prop], 否)","explanation_zh":"擴展基礎核對=(缺, [Mathlib, Module10], 是, env-10, ctx-10, 是, Type, success, [lean_version, core_type_Prop], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187086,"parameters":{"lean_version":"","imports":["Mathlib","Module10"],"imports_declared":true,"environment_id":"env-10","context_id":"ctx-10","source_sha256":"000000000000000000000000000000000000000000000000000000000000000a","core_type":"Type","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-10\",\"core_type\":\"Type\",\"elaboration_status\":\"success\",\"environment_id\":\"env-10\",\"imports\":[\"Mathlib\",\"Module10\"],\"imports_declared\":true,\"lean_version\":\"\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000a\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0087","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.31.0\",\"imports\":[\"Mathlib\",\"Module11\"],\"imports_declared\":true,\"environment_id\":\"env-11\",\"context_id\":\"ctx-11\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000b\",\"core_type\":\"Prop\",\"elaboration_status\":\"failed\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.31.0, [Mathlib, Module11], 是, env-11, ctx-11, 是, Prop, failed, [elaboration_success], 否)","explanation_zh":"擴展基礎核對=(4.31.0, [Mathlib, Module11], 是, env-11, ctx-11, 是, Prop, failed, [elaboration_success], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187087,"parameters":{"lean_version":"4.31.0","imports":["Mathlib","Module11"],"imports_declared":true,"environment_id":"env-11","context_id":"ctx-11","source_sha256":"000000000000000000000000000000000000000000000000000000000000000b","core_type":"Prop","elaboration_status":"failed","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-11\",\"core_type\":\"Prop\",\"elaboration_status\":\"failed\",\"environment_id\":\"env-11\",\"imports\":[\"Mathlib\",\"Module11\"],\"imports_declared\":true,\"lean_version\":\"4.31.0\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000b\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0088","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.32.0\",\"imports\":[],\"imports_declared\":false,\"environment_id\":\"env-12\",\"context_id\":\"ctx-12\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000c\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.32.0, [], 否, env-12, ctx-12, 是, Prop, success, [imports_declaration], 否)","explanation_zh":"擴展基礎核對=(4.32.0, [], 否, env-12, ctx-12, 是, Prop, success, [imports_declaration], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187088,"parameters":{"lean_version":"4.32.0","imports":[],"imports_declared":false,"environment_id":"env-12","context_id":"ctx-12","source_sha256":"000000000000000000000000000000000000000000000000000000000000000c","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-12\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-12\",\"imports\":[],\"imports_declared\":false,\"lean_version\":\"4.32.0\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000c\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0089","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.33.0\",\"imports\":[\"Mathlib\",\"Module13\"],\"imports_declared\":true,\"environment_id\":\"env-13\",\"context_id\":\"ctx-13\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000d\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.33.0, [Mathlib, Module13], 是, env-13, ctx-13, 是, Prop, success, [], 是)","explanation_zh":"擴展基礎核對=(4.33.0, [Mathlib, Module13], 是, env-13, ctx-13, 是, Prop, success, [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187089,"parameters":{"lean_version":"4.33.0","imports":["Mathlib","Module13"],"imports_declared":true,"environment_id":"env-13","context_id":"ctx-13","source_sha256":"000000000000000000000000000000000000000000000000000000000000000d","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-13\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-13\",\"imports\":[\"Mathlib\",\"Module13\"],\"imports_declared\":true,\"lean_version\":\"4.33.0\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000d\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0090","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.34.0\",\"imports\":[\"Mathlib\",\"Module14\"],\"imports_declared\":true,\"environment_id\":\"\",\"context_id\":\"ctx-14\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000e\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.34.0, [Mathlib, Module14], 是, 缺, ctx-14, 是, Prop, success, [environment_id], 否)","explanation_zh":"擴展基礎核對=(4.34.0, [Mathlib, Module14], 是, 缺, ctx-14, 是, Prop, success, [environment_id], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187090,"parameters":{"lean_version":"4.34.0","imports":["Mathlib","Module14"],"imports_declared":true,"environment_id":"","context_id":"ctx-14","source_sha256":"000000000000000000000000000000000000000000000000000000000000000e","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-14\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"\",\"imports\":[\"Mathlib\",\"Module14\"],\"imports_declared\":true,\"lean_version\":\"4.34.0\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000e\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0091","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"\",\"imports\":[\"Mathlib\",\"Module15\"],\"imports_declared\":true,\"environment_id\":\"env-15\",\"context_id\":\"ctx-15\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000f\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(缺, [Mathlib, Module15], 是, env-15, ctx-15, 是, Prop, success, [lean_version], 否)","explanation_zh":"擴展基礎核對=(缺, [Mathlib, Module15], 是, env-15, ctx-15, 是, Prop, success, [lean_version], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187091,"parameters":{"lean_version":"","imports":["Mathlib","Module15"],"imports_declared":true,"environment_id":"env-15","context_id":"ctx-15","source_sha256":"000000000000000000000000000000000000000000000000000000000000000f","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-15\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-15\",\"imports\":[\"Mathlib\",\"Module15\"],\"imports_declared\":true,\"lean_version\":\"\",\"source_sha256\":\"000000000000000000000000000000000000000000000000000000000000000f\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0092","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.36.0\",\"imports\":[],\"imports_declared\":true,\"environment_id\":\"env-16\",\"context_id\":\"\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000010\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.36.0, [], 是, env-16, 缺, 是, Prop, success, [context_id], 否)","explanation_zh":"擴展基礎核對=(4.36.0, [], 是, env-16, 缺, 是, Prop, success, [context_id], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187092,"parameters":{"lean_version":"4.36.0","imports":[],"imports_declared":true,"environment_id":"env-16","context_id":"","source_sha256":"0000000000000000000000000000000000000000000000000000000000000010","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-16\",\"imports\":[],\"imports_declared\":true,\"lean_version\":\"4.36.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000010\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0093","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.37.0\",\"imports\":[\"Mathlib\",\"Module17\"],\"imports_declared\":true,\"environment_id\":\"env-17\",\"context_id\":\"ctx-17\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000011\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.37.0, [Mathlib, Module17], 是, env-17, ctx-17, 是, Prop, success, [], 是)","explanation_zh":"擴展基礎核對=(4.37.0, [Mathlib, Module17], 是, env-17, ctx-17, 是, Prop, success, [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187093,"parameters":{"lean_version":"4.37.0","imports":["Mathlib","Module17"],"imports_declared":true,"environment_id":"env-17","context_id":"ctx-17","source_sha256":"0000000000000000000000000000000000000000000000000000000000000011","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-17\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-17\",\"imports\":[\"Mathlib\",\"Module17\"],\"imports_declared\":true,\"lean_version\":\"4.37.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000011\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0094","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.38.0\",\"imports\":[\"Mathlib\",\"Module18\"],\"imports_declared\":false,\"environment_id\":\"env-18\",\"context_id\":\"ctx-18\",\"source_sha256\":\"bad\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.38.0, [Mathlib, Module18], 否, env-18, ctx-18, 否, Prop, success, [imports_declaration, source_sha256], 否)","explanation_zh":"擴展基礎核對=(4.38.0, [Mathlib, Module18], 否, env-18, ctx-18, 否, Prop, success, [imports_declaration, source_sha256], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187094,"parameters":{"lean_version":"4.38.0","imports":["Mathlib","Module18"],"imports_declared":false,"environment_id":"env-18","context_id":"ctx-18","source_sha256":"bad","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-18\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-18\",\"imports\":[\"Mathlib\",\"Module18\"],\"imports_declared\":false,\"lean_version\":\"4.38.0\",\"source_sha256\":\"bad\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0095","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.39.0\",\"imports\":[\"Mathlib\",\"Module19\"],\"imports_declared\":true,\"environment_id\":\"env-19\",\"context_id\":\"ctx-19\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000013\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.39.0, [Mathlib, Module19], 是, env-19, ctx-19, 是, Prop, success, [], 是)","explanation_zh":"擴展基礎核對=(4.39.0, [Mathlib, Module19], 是, env-19, ctx-19, 是, Prop, success, [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187095,"parameters":{"lean_version":"4.39.0","imports":["Mathlib","Module19"],"imports_declared":true,"environment_id":"env-19","context_id":"ctx-19","source_sha256":"0000000000000000000000000000000000000000000000000000000000000013","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-19\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-19\",\"imports\":[\"Mathlib\",\"Module19\"],\"imports_declared\":true,\"lean_version\":\"4.39.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000013\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0096","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"\",\"imports\":[],\"imports_declared\":true,\"environment_id\":\"env-20\",\"context_id\":\"ctx-20\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000014\",\"core_type\":\"Type\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(缺, [], 是, env-20, ctx-20, 是, Type, success, [lean_version, core_type_Prop], 否)","explanation_zh":"擴展基礎核對=(缺, [], 是, env-20, ctx-20, 是, Type, success, [lean_version, core_type_Prop], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187096,"parameters":{"lean_version":"","imports":[],"imports_declared":true,"environment_id":"env-20","context_id":"ctx-20","source_sha256":"0000000000000000000000000000000000000000000000000000000000000014","core_type":"Type","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-20\",\"core_type\":\"Type\",\"elaboration_status\":\"success\",\"environment_id\":\"env-20\",\"imports\":[],\"imports_declared\":true,\"lean_version\":\"\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000014\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0097","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.41.0\",\"imports\":[\"Mathlib\",\"Module21\"],\"imports_declared\":true,\"environment_id\":\"\",\"context_id\":\"ctx-21\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000015\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.41.0, [Mathlib, Module21], 是, 缺, ctx-21, 是, Prop, success, [environment_id], 否)","explanation_zh":"擴展基礎核對=(4.41.0, [Mathlib, Module21], 是, 缺, ctx-21, 是, Prop, success, [environment_id], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187097,"parameters":{"lean_version":"4.41.0","imports":["Mathlib","Module21"],"imports_declared":true,"environment_id":"","context_id":"ctx-21","source_sha256":"0000000000000000000000000000000000000000000000000000000000000015","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-21\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"\",\"imports\":[\"Mathlib\",\"Module21\"],\"imports_declared\":true,\"lean_version\":\"4.41.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000015\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0098","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.42.0\",\"imports\":[\"Mathlib\",\"Module22\"],\"imports_declared\":true,\"environment_id\":\"env-22\",\"context_id\":\"ctx-22\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000016\",\"core_type\":\"Prop\",\"elaboration_status\":\"failed\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.42.0, [Mathlib, Module22], 是, env-22, ctx-22, 是, Prop, failed, [elaboration_success], 否)","explanation_zh":"擴展基礎核對=(4.42.0, [Mathlib, Module22], 是, env-22, ctx-22, 是, Prop, failed, [elaboration_success], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187098,"parameters":{"lean_version":"4.42.0","imports":["Mathlib","Module22"],"imports_declared":true,"environment_id":"env-22","context_id":"ctx-22","source_sha256":"0000000000000000000000000000000000000000000000000000000000000016","core_type":"Prop","elaboration_status":"failed","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-22\",\"core_type\":\"Prop\",\"elaboration_status\":\"failed\",\"environment_id\":\"env-22\",\"imports\":[\"Mathlib\",\"Module22\"],\"imports_declared\":true,\"lean_version\":\"4.42.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000016\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0099","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.43.0\",\"imports\":[\"Mathlib\",\"Module23\"],\"imports_declared\":true,\"environment_id\":\"env-23\",\"context_id\":\"ctx-23\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000017\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.43.0, [Mathlib, Module23], 是, env-23, ctx-23, 是, Prop, success, [], 是)","explanation_zh":"擴展基礎核對=(4.43.0, [Mathlib, Module23], 是, env-23, ctx-23, 是, Prop, success, [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187099,"parameters":{"lean_version":"4.43.0","imports":["Mathlib","Module23"],"imports_declared":true,"environment_id":"env-23","context_id":"ctx-23","source_sha256":"0000000000000000000000000000000000000000000000000000000000000017","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"ctx-23\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-23\",\"imports\":[\"Mathlib\",\"Module23\"],\"imports_declared\":true,\"lean_version\":\"4.43.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000017\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r07-lean-formal-statement-0100","batch_id":"batch-20261013-advance-20261018-r07-lean-formal-statement-foundations","language":"zh-Hant","source_mko_ids":["mko-lean-formal-statement"],"title_zh":"形式陳述pipeline狀態","stem_zh":"合成pipeline receipt。操作=formal-receipt-completeness；資料={\"lean_version\":\"4.44.0\",\"imports\":[],\"imports_declared\":false,\"environment_id\":\"env-24\",\"context_id\":\"\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000018\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\"}。請依 [version,imports,declared,environment,context,source_hash_valid,core_type,status,missing,complete] 的欄序回答。","answer":{"kind":"expression","value":"(4.44.0, [], 否, env-24, 缺, 是, Prop, success, [imports_declaration, context_id], 否)","explanation_zh":"擴展基礎核對=(4.44.0, [], 否, env-24, 缺, 是, Prop, success, [imports_declaration, context_id], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；合成receipt不是Lean執行；陳述與證明分離；本輪未跑Lean build。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["形式陳述pipeline狀態"]},"variant":{"family_id":"qf-ext18-formal-receipt-completeness","seed":202610187100,"parameters":{"lean_version":"4.44.0","imports":[],"imports_declared":false,"environment_id":"env-24","context_id":"","source_sha256":"0000000000000000000000000000000000000000000000000000000000000018","core_type":"Prop","elaboration_status":"success","domain":"Synthetic_formal_statement_receipt","operation":"formal-receipt-completeness","semantic_template":"qf-ext18-formal-receipt-completeness/{\"context_id\":\"\",\"core_type\":\"Prop\",\"elaboration_status\":\"success\",\"environment_id\":\"env-24\",\"imports\":[],\"imports_declared\":false,\"lean_version\":\"4.44.0\",\"source_sha256\":\"0000000000000000000000000000000000000000000000000000000000000018\"}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}