{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0001","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[0,0,0,0],\"target_event\":[0,1]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 0, 0, 0], [0, 1], [0, 1, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [0, 0, 0, 0], [0, 1], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242001,"parameters":{"source_n":4,"target_n":4,"mapping":[0,0,0,0],"target_event":[0,1],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[0,0,0,0],\"source_n\":4,\"target_event\":[0,1],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0002","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[1,0,0,0],\"target_event\":[1,2]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 0, 0, 0], [1, 2], [0])","explanation_zh":"依賴結構核對=(4, 4, [1, 0, 0, 0], [1, 2], [0])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242002,"parameters":{"source_n":4,"target_n":4,"mapping":[1,0,0,0],"target_event":[1,2],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[1,0,0,0],\"source_n\":4,\"target_event\":[1,2],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0003","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[2,0,0,0],\"target_event\":[2,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 0, 0, 0], [2, 3], [0])","explanation_zh":"依賴結構核對=(4, 4, [2, 0, 0, 0], [2, 3], [0])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242003,"parameters":{"source_n":4,"target_n":4,"mapping":[2,0,0,0],"target_event":[2,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[2,0,0,0],\"source_n\":4,\"target_event\":[2,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0004","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[3,0,0,0],\"target_event\":[0,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 0, 0, 0], [0, 3], [0, 1, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [3, 0, 0, 0], [0, 3], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242004,"parameters":{"source_n":4,"target_n":4,"mapping":[3,0,0,0],"target_event":[0,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[3,0,0,0],\"source_n\":4,\"target_event\":[0,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0005","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[0,1,0,0],\"target_event\":[0,1]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 1, 0, 0], [0, 1], [0, 1, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [0, 1, 0, 0], [0, 1], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242005,"parameters":{"source_n":4,"target_n":4,"mapping":[0,1,0,0],"target_event":[0,1],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[0,1,0,0],\"source_n\":4,\"target_event\":[0,1],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0006","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[1,1,0,0],\"target_event\":[1,2]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 1, 0, 0], [1, 2], [0, 1])","explanation_zh":"依賴結構核對=(4, 4, [1, 1, 0, 0], [1, 2], [0, 1])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242006,"parameters":{"source_n":4,"target_n":4,"mapping":[1,1,0,0],"target_event":[1,2],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[1,1,0,0],\"source_n\":4,\"target_event\":[1,2],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0007","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[2,1,0,0],\"target_event\":[2,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 1, 0, 0], [2, 3], [0])","explanation_zh":"依賴結構核對=(4, 4, [2, 1, 0, 0], [2, 3], [0])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242007,"parameters":{"source_n":4,"target_n":4,"mapping":[2,1,0,0],"target_event":[2,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[2,1,0,0],\"source_n\":4,\"target_event\":[2,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0008","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[3,1,0,0],\"target_event\":[0,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 1, 0, 0], [0, 3], [0, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [3, 1, 0, 0], [0, 3], [0, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242008,"parameters":{"source_n":4,"target_n":4,"mapping":[3,1,0,0],"target_event":[0,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[3,1,0,0],\"source_n\":4,\"target_event\":[0,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0009","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[0,2,0,0],\"target_event\":[0,1]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 2, 0, 0], [0, 1], [0, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [0, 2, 0, 0], [0, 1], [0, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242009,"parameters":{"source_n":4,"target_n":4,"mapping":[0,2,0,0],"target_event":[0,1],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[0,2,0,0],\"source_n\":4,\"target_event\":[0,1],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0010","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[1,2,0,0],\"target_event\":[1,2]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 2, 0, 0], [1, 2], [0, 1])","explanation_zh":"依賴結構核對=(4, 4, [1, 2, 0, 0], [1, 2], [0, 1])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242010,"parameters":{"source_n":4,"target_n":4,"mapping":[1,2,0,0],"target_event":[1,2],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[1,2,0,0],\"source_n\":4,\"target_event\":[1,2],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0011","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[2,2,0,0],\"target_event\":[2,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 2, 0, 0], [2, 3], [0, 1])","explanation_zh":"依賴結構核對=(4, 4, [2, 2, 0, 0], [2, 3], [0, 1])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242011,"parameters":{"source_n":4,"target_n":4,"mapping":[2,2,0,0],"target_event":[2,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[2,2,0,0],\"source_n\":4,\"target_event\":[2,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0012","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[3,2,0,0],\"target_event\":[0,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 2, 0, 0], [0, 3], [0, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [3, 2, 0, 0], [0, 3], [0, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242012,"parameters":{"source_n":4,"target_n":4,"mapping":[3,2,0,0],"target_event":[0,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[3,2,0,0],\"source_n\":4,\"target_event\":[0,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0013","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[0,3,0,0],\"target_event\":[0,1]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 3, 0, 0], [0, 1], [0, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [0, 3, 0, 0], [0, 1], [0, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242013,"parameters":{"source_n":4,"target_n":4,"mapping":[0,3,0,0],"target_event":[0,1],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[0,3,0,0],\"source_n\":4,\"target_event\":[0,1],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0014","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[1,3,0,0],\"target_event\":[1,2]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 3, 0, 0], [1, 2], [0])","explanation_zh":"依賴結構核對=(4, 4, [1, 3, 0, 0], [1, 2], [0])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242014,"parameters":{"source_n":4,"target_n":4,"mapping":[1,3,0,0],"target_event":[1,2],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[1,3,0,0],\"source_n\":4,\"target_event\":[1,2],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0015","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[2,3,0,0],\"target_event\":[2,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 3, 0, 0], [2, 3], [0, 1])","explanation_zh":"依賴結構核對=(4, 4, [2, 3, 0, 0], [2, 3], [0, 1])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242015,"parameters":{"source_n":4,"target_n":4,"mapping":[2,3,0,0],"target_event":[2,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[2,3,0,0],\"source_n\":4,\"target_event\":[2,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0016","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[3,3,0,0],\"target_event\":[0,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 3, 0, 0], [0, 3], [0, 1, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [3, 3, 0, 0], [0, 3], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242016,"parameters":{"source_n":4,"target_n":4,"mapping":[3,3,0,0],"target_event":[0,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[3,3,0,0],\"source_n\":4,\"target_event\":[0,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0017","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[0,0,1,0],\"target_event\":[0,1]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 0, 1, 0], [0, 1], [0, 1, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [0, 0, 1, 0], [0, 1], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242017,"parameters":{"source_n":4,"target_n":4,"mapping":[0,0,1,0],"target_event":[0,1],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[0,0,1,0],\"source_n\":4,\"target_event\":[0,1],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0018","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[1,0,1,0],\"target_event\":[1,2]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 0, 1, 0], [1, 2], [0, 2])","explanation_zh":"依賴結構核對=(4, 4, [1, 0, 1, 0], [1, 2], [0, 2])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242018,"parameters":{"source_n":4,"target_n":4,"mapping":[1,0,1,0],"target_event":[1,2],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[1,0,1,0],\"source_n\":4,\"target_event\":[1,2],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0019","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[2,0,1,0],\"target_event\":[2,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 0, 1, 0], [2, 3], [0])","explanation_zh":"依賴結構核對=(4, 4, [2, 0, 1, 0], [2, 3], [0])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242019,"parameters":{"source_n":4,"target_n":4,"mapping":[2,0,1,0],"target_event":[2,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[2,0,1,0],\"source_n\":4,\"target_event\":[2,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0020","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[3,0,1,0],\"target_event\":[0,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 0, 1, 0], [0, 3], [0, 1, 3])","explanation_zh":"依賴結構核對=(4, 4, [3, 0, 1, 0], [0, 3], [0, 1, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242020,"parameters":{"source_n":4,"target_n":4,"mapping":[3,0,1,0],"target_event":[0,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[3,0,1,0],\"source_n\":4,\"target_event\":[0,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0021","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[0,1,1,0],\"target_event\":[0,1]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 1, 1, 0], [0, 1], [0, 1, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [0, 1, 1, 0], [0, 1], [0, 1, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242021,"parameters":{"source_n":4,"target_n":4,"mapping":[0,1,1,0],"target_event":[0,1],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[0,1,1,0],\"source_n\":4,\"target_event\":[0,1],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0022","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[1,1,1,0],\"target_event\":[1,2]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 1, 1, 0], [1, 2], [0, 1, 2])","explanation_zh":"依賴結構核對=(4, 4, [1, 1, 1, 0], [1, 2], [0, 1, 2])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242022,"parameters":{"source_n":4,"target_n":4,"mapping":[1,1,1,0],"target_event":[1,2],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[1,1,1,0],\"source_n\":4,\"target_event\":[1,2],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0023","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[2,1,1,0],\"target_event\":[2,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 1, 1, 0], [2, 3], [0])","explanation_zh":"依賴結構核對=(4, 4, [2, 1, 1, 0], [2, 3], [0])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242023,"parameters":{"source_n":4,"target_n":4,"mapping":[2,1,1,0],"target_event":[2,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[2,1,1,0],\"source_n\":4,\"target_event\":[2,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0024","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[3,1,1,0],\"target_event\":[0,3]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 1, 1, 0], [0, 3], [0, 3])","explanation_zh":"依賴結構核對=(4, 4, [3, 1, 1, 0], [0, 3], [0, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242024,"parameters":{"source_n":4,"target_n":4,"mapping":[3,1,1,0],"target_event":[0,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[3,1,1,0],\"source_n\":4,\"target_event\":[0,3],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0025","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-preimage；資料={\"source_n\":4,\"target_n\":4,\"mapping\":[0,2,1,0],\"target_event\":[0,1]}。請依 [source_n,target_n,mapping,target_event,preimage] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 2, 1, 0], [0, 1], [0, 2, 3])","explanation_zh":"依賴結構核對=(4, 4, [0, 2, 1, 0], [0, 1], [0, 2, 3])；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-preimage","seed":202610242025,"parameters":{"source_n":4,"target_n":4,"mapping":[0,2,1,0],"target_event":[0,1],"domain":"Complete_finite_measurable_spaces","operation":"measurable-preimage","semantic_template":"qf-mod24-measurable-preimage/{\"mapping\":[0,2,1,0],\"source_n\":4,\"target_event\":[0,1],\"target_n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0026","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[0,0,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242026,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,0,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[0,0,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0],[1,2,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0027","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[1,0,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 0, 0, 0], [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [0], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [1, 0, 0, 0], [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [0], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242027,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,0,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[1,0,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0028","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,1],[2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[2,0,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 0, 0, 0], [[[], [], 是], [[0], [1, 2, 3], 否], [[1], [], 是], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 否], [[1, 3], [], 是], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [2, 0, 0, 0], [[[], [], 是], [[0], [1, 2, 3], 否], [[1], [], 是], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 2, 3], 否], [[1, 3], [], 是], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242028,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,0,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[2,0,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1],[2,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0029","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[3,0,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 0, 0, 0], [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [3, 0, 0, 0], [[[], [], 是], [[0], [1, 2, 3], 是], [[1], [], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242029,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,0,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[3,0,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0030","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,2],[1,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[0,1,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 1, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 否], [[1], [1], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 否], [[1, 3], [1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [0, 1, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 否], [[1], [1], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 否], [[1, 3], [1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242030,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,1,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[0,1,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,2],[1,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0031","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[1,1,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 1, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [0, 1], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [1, 1, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [0, 1], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242031,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,1,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[1,1,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0032","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,1,2],[3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[2,1,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 1, 0, 0], [[[], [], 是], [[0], [2, 3], 否], [[1], [1], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 2, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [1], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [2, 1, 0, 0], [[[], [], 是], [[0], [2, 3], 否], [[1], [1], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 2, 3], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [1], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 2, 3], 否], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242032,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,1,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[2,1,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0033","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[3,1,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 1, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [1], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [3, 1, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [1], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242033,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,1,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[3,1,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0034","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[1],[0,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[0,2,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 2, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [0, 2, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242034,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,2,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[0,2,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,2,3],[1]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0035","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[1,2,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 2, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [1, 2, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0, 1], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242035,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,2,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[1,2,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0036","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[2],[0,1,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[2,2,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 2, 0, 0], [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [0, 1], 否], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [], 是], [[0, 1, 3], [2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [2, 2, 0, 0], [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [0, 1], 否], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [2, 3], 否], [[1, 3], [], 是], [[0, 1, 3], [2, 3], 否], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242036,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,2,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[2,2,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,3],[2]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0037","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[3,2,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 2, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [1], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [3, 2, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [1], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [1], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 2, 3], 是], [[1, 3], [0], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242037,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,2,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[3,2,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0038","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[1,2],[0,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[0,3,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 3, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 否], [[1], [], 是], [[0, 1], [0, 2, 3], 否], [[2], [], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [0, 3, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 否], [[1], [], 是], [[0, 1], [0, 2, 3], 否], [[2], [], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242038,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[1,2],[0,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,3,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[0,3,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,3],[1,2]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0039","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[1,3,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 3, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [1, 3, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [0], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [1, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242039,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,3,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[1,3,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0040","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[2,3,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 3, 0, 0], [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [0], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 2, 3], 是], [[1, 3], [1], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [2, 3, 0, 0], [[[], [], 是], [[0], [2, 3], 否], [[1], [], 是], [[0, 1], [2, 3], 否], [[2], [0], 是], [[0, 2], [0, 2, 3], 否], [[1, 2], [0], 是], [[0, 1, 2], [0, 2, 3], 否], [[3], [1], 否], [[0, 3], [1, 2, 3], 是], [[1, 3], [1], 否], [[0, 1, 3], [1, 2, 3], 是], [[2, 3], [0, 1], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242040,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,3,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[2,3,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0],[1,2,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0041","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[3,3,0,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 3, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [2, 3], 是], [[3], [0, 1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [3, 3, 0, 0], [[[], [], 是], [[0], [2, 3], 是], [[1], [], 是], [[0, 1], [2, 3], 是], [[2], [], 是], [[0, 2], [2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [2, 3], 是], [[3], [0, 1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242041,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,3,0,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[3,3,0,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0042","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,1],[2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[0,0,1,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 0, 1, 0], [[[], [], 是], [[0], [0, 1, 3], 否], [[1], [2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 3], 否], [[1, 2], [2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 3], 否], [[1, 3], [2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [0, 0, 1, 0], [[[], [], 是], [[0], [0, 1, 3], 否], [[1], [2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 3], 否], [[1, 2], [2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 3], 否], [[1, 3], [2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242042,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,0,1,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[0,0,1,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1],[2,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0043","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[1,0,1,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 0, 1, 0], [[[], [], 是], [[0], [1, 3], 是], [[1], [0, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 是], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [1, 0, 1, 0], [[[], [], 是], [[0], [1, 3], 是], [[1], [0, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 是], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242043,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,0,1,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[1,0,1,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0044","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,2],[1,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[2,0,1,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 0, 1, 0], [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 1, 3], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [2], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [2, 0, 1, 0], [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 1, 3], 否], [[1, 2], [0, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1, 3], 是], [[1, 3], [2], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242044,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,0,1,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[2,0,1,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,2],[1,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0045","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[3,0,1,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 0, 1, 0], [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 是], [[1, 2], [2], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 1, 3], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [3, 0, 1, 0], [[[], [], 是], [[0], [1, 3], 是], [[1], [2], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [1, 3], 是], [[1, 2], [2], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 1, 3], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [0, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242045,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,0,1,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[3,0,1,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0046","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,1,2],[3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[0,1,1,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 1, 1, 0], [[[], [], 是], [[0], [0, 3], 否], [[1], [1, 2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 3], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [0, 1, 1, 0], [[[], [], 是], [[0], [0, 3], 否], [[1], [1, 2], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 3], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242046,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,1,1,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[0,1,1,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0047","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[1,1,1,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [1, 1, 1, 0], [[[], [], 是], [[0], [3], 是], [[1], [0, 1, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 是], [[1, 2], [0, 1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 是], [[1, 3], [0, 1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [1, 1, 1, 0], [[[], [], 是], [[0], [3], 是], [[1], [0, 1, 2], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 是], [[1, 2], [0, 1, 2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 是], [[1, 3], [0, 1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242047,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[1,1,1,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[1,1,1,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0048","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[1],[0,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[2,1,1,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [2, 1, 1, 0], [[[], [], 是], [[0], [3], 否], [[1], [1, 2], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [2, 1, 1, 0], [[[], [], 是], [[0], [3], 否], [[1], [1, 2], 否], [[0, 1], [1, 2, 3], 否], [[2], [0], 否], [[0, 2], [0, 3], 否], [[1, 2], [0, 1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [3], 否], [[1, 3], [1, 2], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0], 否], [[0, 2, 3], [0, 3], 否], [[1, 2, 3], [0, 1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242048,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[2,1,1,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[2,1,1,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,2,3],[1]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0049","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[3,1,1,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [3, 1, 1, 0], [[[], [], 是], [[0], [3], 是], [[1], [1, 2], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 是], [[1, 2], [1, 2], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 3], 是], [[1, 3], [0, 1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)","explanation_zh":"依賴結構核對=(4, 4, [3, 1, 1, 0], [[[], [], 是], [[0], [3], 是], [[1], [1, 2], 是], [[0, 1], [1, 2, 3], 是], [[2], [], 是], [[0, 2], [3], 是], [[1, 2], [1, 2], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0, 3], 是], [[1, 3], [0, 1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0], 是], [[0, 2, 3], [0, 3], 是], [[1, 2, 3], [0, 1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242049,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[3,1,1,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[3,1,1,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0050","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-map-audit；資料={\"source_n\":4,\"target_n\":4,\"source_sigma\":[[],[2],[0,1,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"mapping\":[0,2,1,0]}。請依 [source_n,target_n,mapping,preimage_rows,measurable] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, [0, 2, 1, 0], [[[], [], 是], [[0], [0, 3], 否], [[1], [2], 是], [[0, 1], [0, 2, 3], 否], [[2], [1], 否], [[0, 2], [0, 1, 3], 是], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 否], [[1, 3], [2], 是], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)","explanation_zh":"依賴結構核對=(4, 4, [0, 2, 1, 0], [[[], [], 是], [[0], [0, 3], 否], [[1], [2], 是], [[0, 1], [0, 2, 3], 否], [[2], [1], 否], [[0, 2], [0, 1, 3], 是], [[1, 2], [1, 2], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 3], 否], [[1, 3], [2], 是], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1], 否], [[0, 2, 3], [0, 1, 3], 是], [[1, 2, 3], [1, 2], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-map-audit","seed":202610242050,"parameters":{"source_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"mapping":[0,2,1,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-map-audit","semantic_template":"qf-mod24-measurable-map-audit/{\"mapping\":[0,2,1,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,3],[2]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0051","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0],[1,2,3,4,5],[0,1,2,3,4,5]],\"event\":[0]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [1, 0, 0, 0, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [0], [1, 0, 0, 0, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242051,"parameters":{"source_n":6,"source_sigma":[[],[0],[1,2,3,4,5],[0,1,2,3,4,5]],"event":[0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0],[1,2,3,4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0052","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[1],[0,2,3,4,5],[0,1,2,3,4,5]],\"event\":[1]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [1], [0, 1, 0, 0, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [1], [0, 1, 0, 0, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242052,"parameters":{"source_n":6,"source_sigma":[[],[1],[0,2,3,4,5],[0,1,2,3,4,5]],"event":[1],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[1],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,2,3,4,5],[1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0053","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,1],[2,3,4,5],[0,1,2,3,4,5]],\"event\":[0,1]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1], [1, 1, 0, 0, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [0, 1], [1, 1, 0, 0, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242053,"parameters":{"source_n":6,"source_sigma":[[],[0,1],[2,3,4,5],[0,1,2,3,4,5]],"event":[0,1],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0,1],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1],[2,3,4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0054","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[2],[0,1,3,4,5],[0,1,2,3,4,5]],\"event\":[0]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [1, 0, 0, 0, 0, 0], 否)","explanation_zh":"依賴結構核對=(6, [0], [1, 0, 0, 0, 0, 0], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242054,"parameters":{"source_n":6,"source_sigma":[[],[2],[0,1,3,4,5],[0,1,2,3,4,5]],"event":[0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,3,4,5],[2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0055","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,2],[1,3,4,5],[0,1,2,3,4,5]],\"event\":[0,2]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2], [1, 0, 1, 0, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [0, 2], [1, 0, 1, 0, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242055,"parameters":{"source_n":6,"source_sigma":[[],[0,2],[1,3,4,5],[0,1,2,3,4,5]],"event":[0,2],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0,2],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,2],[1,3,4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0056","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[1,2],[0,3,4,5],[0,1,2,3,4,5]],\"event\":[1,2]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2], [0, 1, 1, 0, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [1, 2], [0, 1, 1, 0, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242056,"parameters":{"source_n":6,"source_sigma":[[],[1,2],[0,3,4,5],[0,1,2,3,4,5]],"event":[1,2],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[1,2],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,3,4,5],[1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0057","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,1,2],[3,4,5],[0,1,2,3,4,5]],\"event\":[0]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [1, 0, 0, 0, 0, 0], 否)","explanation_zh":"依賴結構核對=(6, [0], [1, 0, 0, 0, 0, 0], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242057,"parameters":{"source_n":6,"source_sigma":[[],[0,1,2],[3,4,5],[0,1,2,3,4,5]],"event":[0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,2],[3,4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0058","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[3],[0,1,2,4,5],[0,1,2,3,4,5]],\"event\":[3]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [3], [0, 0, 0, 1, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [3], [0, 0, 0, 1, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242058,"parameters":{"source_n":6,"source_sigma":[[],[3],[0,1,2,4,5],[0,1,2,3,4,5]],"event":[3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[3],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,2,4,5],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0059","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,3],[1,2,4,5],[0,1,2,3,4,5]],\"event\":[0,3]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3], [1, 0, 0, 1, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [0, 3], [1, 0, 0, 1, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242059,"parameters":{"source_n":6,"source_sigma":[[],[0,3],[1,2,4,5],[0,1,2,3,4,5]],"event":[0,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0,3],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,3],[1,2,4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0060","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[1,3],[0,2,4,5],[0,1,2,3,4,5]],\"event\":[0]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [1, 0, 0, 0, 0, 0], 否)","explanation_zh":"依賴結構核對=(6, [0], [1, 0, 0, 0, 0, 0], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242060,"parameters":{"source_n":6,"source_sigma":[[],[1,3],[0,2,4,5],[0,1,2,3,4,5]],"event":[0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,2,4,5],[1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0061","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,1,3],[2,4,5],[0,1,2,3,4,5]],\"event\":[0,1,3]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3], [1, 1, 0, 1, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [0, 1, 3], [1, 1, 0, 1, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242061,"parameters":{"source_n":6,"source_sigma":[[],[0,1,3],[2,4,5],[0,1,2,3,4,5]],"event":[0,1,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0,1,3],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,3],[2,4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0062","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[2,3],[0,1,4,5],[0,1,2,3,4,5]],\"event\":[2,3]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [2, 3], [0, 0, 1, 1, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [2, 3], [0, 0, 1, 1, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242062,"parameters":{"source_n":6,"source_sigma":[[],[2,3],[0,1,4,5],[0,1,2,3,4,5]],"event":[2,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[2,3],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,4,5],[2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0063","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,2,3],[1,4,5],[0,1,2,3,4,5]],\"event\":[0]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [1, 0, 0, 0, 0, 0], 否)","explanation_zh":"依賴結構核對=(6, [0], [1, 0, 0, 0, 0, 0], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242063,"parameters":{"source_n":6,"source_sigma":[[],[0,2,3],[1,4,5],[0,1,2,3,4,5]],"event":[0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,2,3],[1,4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0064","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[1,2,3],[0,4,5],[0,1,2,3,4,5]],\"event\":[1,2,3]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2, 3], [0, 1, 1, 1, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [1, 2, 3], [0, 1, 1, 1, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242064,"parameters":{"source_n":6,"source_sigma":[[],[1,2,3],[0,4,5],[0,1,2,3,4,5]],"event":[1,2,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[1,2,3],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,4,5],[1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0065","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,1,2,3],[4,5],[0,1,2,3,4,5]],\"event\":[0,1,2,3]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 3], [1, 1, 1, 1, 0, 0], 是)","explanation_zh":"依賴結構核對=(6, [0, 1, 2, 3], [1, 1, 1, 1, 0, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242065,"parameters":{"source_n":6,"source_sigma":[[],[0,1,2,3],[4,5],[0,1,2,3,4,5]],"event":[0,1,2,3],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0,1,2,3],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,2,3],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0066","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[4],[0,1,2,3,5],[0,1,2,3,4,5]],\"event\":[0]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [1, 0, 0, 0, 0, 0], 否)","explanation_zh":"依賴結構核對=(6, [0], [1, 0, 0, 0, 0, 0], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242066,"parameters":{"source_n":6,"source_sigma":[[],[4],[0,1,2,3,5],[0,1,2,3,4,5]],"event":[0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,2,3,5],[4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0067","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,4],[1,2,3,5],[0,1,2,3,4,5]],\"event\":[0,4]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 4], [1, 0, 0, 0, 1, 0], 是)","explanation_zh":"依賴結構核對=(6, [0, 4], [1, 0, 0, 0, 1, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242067,"parameters":{"source_n":6,"source_sigma":[[],[0,4],[1,2,3,5],[0,1,2,3,4,5]],"event":[0,4],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0,4],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,4],[1,2,3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0068","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[1,4],[0,2,3,5],[0,1,2,3,4,5]],\"event\":[1,4]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4], [0, 1, 0, 0, 1, 0], 是)","explanation_zh":"依賴結構核對=(6, [1, 4], [0, 1, 0, 0, 1, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242068,"parameters":{"source_n":6,"source_sigma":[[],[1,4],[0,2,3,5],[0,1,2,3,4,5]],"event":[1,4],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[1,4],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,2,3,5],[1,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0069","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,1,4],[2,3,5],[0,1,2,3,4,5]],\"event\":[0]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [1, 0, 0, 0, 0, 0], 否)","explanation_zh":"依賴結構核對=(6, [0], [1, 0, 0, 0, 0, 0], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242069,"parameters":{"source_n":6,"source_sigma":[[],[0,1,4],[2,3,5],[0,1,2,3,4,5]],"event":[0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,4],[2,3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0070","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[2,4],[0,1,3,5],[0,1,2,3,4,5]],\"event\":[2,4]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [2, 4], [0, 0, 1, 0, 1, 0], 是)","explanation_zh":"依賴結構核對=(6, [2, 4], [0, 0, 1, 0, 1, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242070,"parameters":{"source_n":6,"source_sigma":[[],[2,4],[0,1,3,5],[0,1,2,3,4,5]],"event":[2,4],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[2,4],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,3,5],[2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0071","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,2,4],[1,3,5],[0,1,2,3,4,5]],\"event\":[0,2,4]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 4], [1, 0, 1, 0, 1, 0], 是)","explanation_zh":"依賴結構核對=(6, [0, 2, 4], [1, 0, 1, 0, 1, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242071,"parameters":{"source_n":6,"source_sigma":[[],[0,2,4],[1,3,5],[0,1,2,3,4,5]],"event":[0,2,4],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0,2,4],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,2,4],[1,3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0072","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[1,2,4],[0,3,5],[0,1,2,3,4,5]],\"event\":[0]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [1, 0, 0, 0, 0, 0], 否)","explanation_zh":"依賴結構核對=(6, [0], [1, 0, 0, 0, 0, 0], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242072,"parameters":{"source_n":6,"source_sigma":[[],[1,2,4],[0,3,5],[0,1,2,3,4,5]],"event":[0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,3,5],[1,2,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0073","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,1,2,4],[3,5],[0,1,2,3,4,5]],\"event\":[0,1,2,4]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 4], [1, 1, 1, 0, 1, 0], 是)","explanation_zh":"依賴結構核對=(6, [0, 1, 2, 4], [1, 1, 1, 0, 1, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242073,"parameters":{"source_n":6,"source_sigma":[[],[0,1,2,4],[3,5],[0,1,2,3,4,5]],"event":[0,1,2,4],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0,1,2,4],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,2,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0074","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[3,4],[0,1,2,5],[0,1,2,3,4,5]],\"event\":[3,4]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [3, 4], [0, 0, 0, 1, 1, 0], 是)","explanation_zh":"依賴結構核對=(6, [3, 4], [0, 0, 0, 1, 1, 0], 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242074,"parameters":{"source_n":6,"source_sigma":[[],[3,4],[0,1,2,5],[0,1,2,3,4,5]],"event":[3,4],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[3,4],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,1,2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0075","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-indicator-audit；資料={\"source_n\":6,\"source_sigma\":[[],[0,3,4],[1,2,5],[0,1,2,3,4,5]],\"event\":[0]}。請依 [source_n,event,indicator_mapping,measurable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [1, 0, 0, 0, 0, 0], 否)","explanation_zh":"依賴結構核對=(6, [0], [1, 0, 0, 0, 0, 0], 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-indicator-audit","seed":202610242075,"parameters":{"source_n":6,"source_sigma":[[],[0,3,4],[1,2,5],[0,1,2,3,4,5]],"event":[0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-indicator-audit","semantic_template":"qf-mod24-measurable-indicator-audit/{\"event\":[0],\"source_n\":6,\"source_sigma\":[[],[0,1,2,3,4,5],[0,3,4],[1,2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0076","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[0,0,0,0],\"second\":[1,1,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242076,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[0,0,0,0],"second":[1,1,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[0,0,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[1,1,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0],[1,2,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0077","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[1,0,0,0],\"second\":[2,1,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [1, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [0], 是], [[0, 1], [0], 是], [[2], [1, 2, 3], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0], 是], [[0, 1, 3], [0], 是], [[2, 3], [1, 2, 3], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [1, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [0], 是], [[0, 1], [0], 是], [[2], [1, 2, 3], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0], 是], [[0, 1, 3], [0], 是], [[2, 3], [1, 2, 3], 是], [[0, 2, 3], [1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242077,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[1,0,0,0],"second":[2,1,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[1,0,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[2,1,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0078","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,1],[2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[2,0,0,0],\"second\":[3,1,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [2, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0], 否], [[0, 2], [0], 否], [[1, 2], [0], 否], [[0, 1, 2], [0], 否], [[3], [1, 2, 3], 否], [[0, 3], [1, 2, 3], 否], [[1, 3], [1, 2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [2, 3, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0], 否], [[0, 2], [0], 否], [[1, 2], [0], 否], [[0, 1, 2], [0], 否], [[3], [1, 2, 3], 否], [[0, 3], [1, 2, 3], 否], [[1, 3], [1, 2, 3], 否], [[0, 1, 3], [1, 2, 3], 否], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242078,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[2,0,0,0],"second":[3,1,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[2,0,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[3,1,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1],[2,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0079","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[3,0,0,0],\"second\":[0,2,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242079,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[3,0,0,0],"second":[0,2,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[3,0,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[0,2,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0080","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,2],[1,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[0,1,0,0],\"second\":[1,2,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [1, 2, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 2, 3], 否], [[0, 1], [0, 2, 3], 否], [[2], [1], 否], [[0, 2], [1], 否], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1], 否], [[0, 2, 3], [1], 否], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [1, 2, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 2, 3], 否], [[0, 1], [0, 2, 3], 否], [[2], [1], 否], [[0, 2], [1], 否], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 2, 3], 否], [[0, 1, 3], [0, 2, 3], 否], [[2, 3], [1], 否], [[0, 2, 3], [1], 否], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242080,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[0,1,0,0],"second":[1,2,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[0,1,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[1,2,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,2],[1,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0081","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[1,1,0,0],\"second\":[2,2,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242081,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[1,1,0,0],"second":[2,2,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[1,1,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[2,2,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0082","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,1,2],[3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[2,1,0,0],\"second\":[3,2,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [2, 2, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1], 否], [[3], [2, 3], 否], [[0, 3], [2, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [2, 3], 否], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [2, 2, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1], 否], [[3], [2, 3], 否], [[0, 3], [2, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [2, 3], 否], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242082,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[2,1,0,0],"second":[3,2,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[2,1,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[3,2,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0083","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[3,1,0,0],\"second\":[0,3,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [0, 3, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [0, 3, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242083,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[3,1,0,0],"second":[0,3,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[3,1,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[0,3,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0084","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[1],[0,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[0,2,0,0],\"second\":[1,3,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [1, 2, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 2, 3], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [1], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 2, 3], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [1, 2, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 2, 3], 是], [[0, 1], [0, 2, 3], 是], [[2], [1], 是], [[0, 2], [1], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 2, 3], 是], [[0, 1, 3], [0, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [1], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242084,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[0,2,0,0],"second":[1,3,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[0,2,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[1,3,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,2,3],[1]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0085","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[1,2,0,0],\"second\":[2,3,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [3, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [1, 2, 3], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [1, 2, 3], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0], 是], [[1, 3], [0], 是], [[0, 1, 3], [0], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [3, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [1, 2, 3], 是], [[0, 2], [1, 2, 3], 是], [[1, 2], [1, 2, 3], 是], [[0, 1, 2], [1, 2, 3], 是], [[3], [0], 是], [[0, 3], [0], 是], [[1, 3], [0], 是], [[0, 1, 3], [0], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242085,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[1,2,0,0],"second":[2,3,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[1,2,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[2,3,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0086","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[2],[0,1,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[2,2,0,0],\"second\":[3,3,2,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [2, 2, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1], 否], [[3], [2, 3], 否], [[0, 3], [2, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [2, 3], 否], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [2, 2, 3, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1], 否], [[0, 2], [0, 1], 否], [[1, 2], [0, 1], 否], [[0, 1, 2], [0, 1], 否], [[3], [2, 3], 否], [[0, 3], [2, 3], 否], [[1, 3], [2, 3], 否], [[0, 1, 3], [2, 3], 否], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242086,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[2,2,0,0],"second":[3,3,2,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[2,2,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[3,3,2,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,3],[2]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0087","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[3,2,0,0],\"second\":[0,0,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [0, 3, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [0, 3, 0, 0], [[[], [], 是], [[0], [0, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 2, 3], 是], [[3], [1], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242087,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[3,2,0,0],"second":[0,0,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[3,2,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[0,0,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0088","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[1,2],[0,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[0,3,0,0],\"second\":[1,0,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [1, 0, 1, 1], [[[], [], 是], [[0], [1], 否], [[1], [0, 2, 3], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1], 否], [[1, 2], [0, 2, 3], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1], 否], [[1, 3], [0, 2, 3], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [1, 0, 1, 1], [[[], [], 是], [[0], [1], 否], [[1], [0, 2, 3], 否], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [1], 否], [[1, 2], [0, 2, 3], 否], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [1], 否], [[1, 3], [0, 2, 3], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [1], 否], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242088,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[1,2],[0,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[0,3,0,0],"second":[1,0,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[0,3,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[1,0,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,3],[1,2]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0089","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[1,3,0,0],\"second\":[2,0,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [0, 0, 2, 2], [[[], [], 是], [[0], [0, 1], 是], [[1], [], 是], [[0, 1], [0, 1], 是], [[2], [2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1], 是], [[2, 3], [2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [0, 0, 2, 2], [[[], [], 是], [[0], [0, 1], 是], [[1], [], 是], [[0, 1], [0, 1], 是], [[2], [2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1], 是], [[2, 3], [2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242089,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[1,3,0,0],"second":[2,0,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[1,3,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[2,0,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0090","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[2,3,0,0],\"second\":[3,0,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [3, 0, 3, 3], [[[], [], 是], [[0], [1], 否], [[1], [], 是], [[0, 1], [1], 否], [[2], [], 是], [[0, 2], [1], 否], [[1, 2], [], 是], [[0, 1, 2], [1], 否], [[3], [0, 2, 3], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 2, 3], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 2, 3], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [3, 0, 3, 3], [[[], [], 是], [[0], [1], 否], [[1], [], 是], [[0, 1], [1], 否], [[2], [], 是], [[0, 2], [1], 否], [[1, 2], [], 是], [[0, 1, 2], [1], 否], [[3], [0, 2, 3], 否], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [0, 2, 3], 否], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 2, 3], 否], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 2, 3], 否], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242090,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[2,3,0,0],"second":[3,0,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[2,3,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[3,0,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0],[1,2,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0091","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[3,3,0,0],\"second\":[0,1,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [0, 0, 0, 0], [[[], [], 是], [[0], [0, 1, 2, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242091,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[3,3,0,0],"second":[0,1,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[3,3,0,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[0,1,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0092","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,1],[2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[0,0,1,0],\"second\":[1,1,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 否)","explanation_zh":"依賴結構核對=(否, 是, [1, 1, 1, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 1, 2, 3], 是], [[0, 1], [0, 1, 2, 3], 是], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [], 是], [[0, 2, 3], [], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242092,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0,1],[2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[0,0,1,0],"second":[1,1,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[0,0,1,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[1,1,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1],[2,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0093","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[1,0,1,0],\"second\":[2,1,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [1, 2, 1, 2], [[[], [], 是], [[0], [], 是], [[1], [0, 2], 是], [[0, 1], [0, 2], 是], [[2], [1, 3], 是], [[0, 2], [1, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 2], 是], [[2, 3], [1, 3], 是], [[0, 2, 3], [1, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [1, 2, 1, 2], [[[], [], 是], [[0], [], 是], [[1], [0, 2], 是], [[0, 1], [0, 2], 是], [[2], [1, 3], 是], [[0, 2], [1, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 2], 是], [[0, 1, 3], [0, 2], 是], [[2, 3], [1, 3], 是], [[0, 2, 3], [1, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242093,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[1,0,1,0],"second":[2,1,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[1,0,1,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[2,1,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0094","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,2],[1,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[2,0,1,0],\"second\":[3,1,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [3, 3, 1, 3], [[[], [], 是], [[0], [], 是], [[1], [2], 否], [[0, 1], [2], 否], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [2], 否], [[0, 1, 2], [2], 否], [[3], [0, 1, 3], 否], [[0, 3], [0, 1, 3], 否], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [3, 3, 1, 3], [[[], [], 是], [[0], [], 是], [[1], [2], 否], [[0, 1], [2], 否], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [2], 否], [[0, 1, 2], [2], 否], [[3], [0, 1, 3], 否], [[0, 3], [0, 1, 3], 否], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [0, 1, 3], 否], [[0, 2, 3], [0, 1, 3], 否], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242094,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0,2],[1,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[2,0,1,0],"second":[3,1,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[2,0,1,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[3,1,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,2],[1,3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0095","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[3,0,1,0],\"second\":[0,2,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [0, 0, 2, 0], [[[], [], 是], [[0], [0, 1, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 3], 是], [[2], [2], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 3], 是], [[2, 3], [2], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [0, 0, 2, 0], [[[], [], 是], [[0], [0, 1, 3], 是], [[1], [], 是], [[0, 1], [0, 1, 3], 是], [[2], [2], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [2], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [0, 1, 3], 是], [[1, 3], [], 是], [[0, 1, 3], [0, 1, 3], 是], [[2, 3], [2], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242095,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[3,0,1,0],"second":[0,2,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[3,0,1,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[0,2,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0096","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0,1,2],[3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[0,1,1,0],\"second\":[1,2,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [1, 2, 2, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 3], 否], [[0, 1], [0, 3], 否], [[2], [1, 2], 否], [[0, 2], [1, 2], 否], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [1, 2], 否], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [1, 2, 2, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 3], 否], [[0, 1], [0, 3], 否], [[2], [1, 2], 否], [[0, 2], [1, 2], 否], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 3], 否], [[2, 3], [1, 2], 否], [[0, 2, 3], [1, 2], 否], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242096,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0,1,2],[3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[0,1,1,0],"second":[1,2,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[0,1,1,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[1,2,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0097","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[1,1,1,0],\"second\":[2,2,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [2, 2, 2, 2], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [0, 1, 2, 3], 是], [[0, 2], [0, 1, 2, 3], 是], [[1, 2], [0, 1, 2, 3], 是], [[0, 1, 2], [0, 1, 2, 3], 是], [[3], [], 是], [[0, 3], [], 是], [[1, 3], [], 是], [[0, 1, 3], [], 是], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242097,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[1,1,1,0],"second":[2,2,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[1,1,1,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[2,2,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0098","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[1],[0,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[2,1,1,0],\"second\":[3,2,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [3, 2, 2, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [1, 2], 否], [[0, 2], [1, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [1, 2], 否], [[3], [0, 3], 否], [[0, 3], [0, 3], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 3], 否], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [3, 2, 2, 3], [[[], [], 是], [[0], [], 是], [[1], [], 是], [[0, 1], [], 是], [[2], [1, 2], 否], [[0, 2], [1, 2], 否], [[1, 2], [1, 2], 否], [[0, 1, 2], [1, 2], 否], [[3], [0, 3], 否], [[0, 3], [0, 3], 否], [[1, 3], [0, 3], 否], [[0, 1, 3], [0, 3], 否], [[2, 3], [0, 1, 2, 3], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242098,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[1],[0,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[2,1,1,0],"second":[3,2,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[2,1,1,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[3,2,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,2,3],[1]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0099","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[3,1,1,0],\"second\":[0,3,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(是, 是, [0, 3, 3, 0], [[[], [], 是], [[0], [0, 3], 是], [[1], [], 是], [[0, 1], [0, 3], 是], [[2], [], 是], [[0, 2], [0, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 3], 是], [[3], [1, 2], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1, 2], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)","explanation_zh":"依賴結構核對=(是, 是, [0, 3, 3, 0], [[[], [], 是], [[0], [0, 3], 是], [[1], [], 是], [[0, 1], [0, 3], 是], [[2], [], 是], [[0, 2], [0, 3], 是], [[1, 2], [], 是], [[0, 1, 2], [0, 3], 是], [[3], [1, 2], 是], [[0, 3], [0, 1, 2, 3], 是], [[1, 3], [1, 2], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1, 2], 是], [[0, 2, 3], [0, 1, 2, 3], 是], [[1, 2, 3], [1, 2], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 是, 是)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242099,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[3,1,1,0],"second":[0,3,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[3,1,1,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[0,3,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261024-r02-measurable-function-0100","batch_id":"batch-20261013-advance-20261024-r02-measurable-function-foundations","language":"zh-Hant","source_mko_ids":["mko-measurable-function"],"title_zh":"有限可測函數","stem_zh":"完整有限來源與目標sigma代數。操作=measurable-composition-audit；資料={\"source_n\":4,\"middle_n\":4,\"target_n\":4,\"source_sigma\":[[],[2],[0,1,3],[0,1,2,3]],\"middle_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"target_sigma\":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],\"first\":[0,2,1,0],\"second\":[1,3,3,0]}。請依 [first_measurable,second_measurable,composite_mapping,composite_rows,composite_measurable,composition_theorem_consistent] 欄序回答。","answer":{"kind":"expression","value":"(否, 是, [1, 3, 3, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 3], 否], [[0, 1], [0, 3], 否], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 3], 否], [[3], [1, 2], 否], [[0, 3], [1, 2], 否], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [1, 2], 否], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)","explanation_zh":"依賴結構核對=(否, 是, [1, 3, 3, 1], [[[], [], 是], [[0], [], 是], [[1], [0, 3], 否], [[0, 1], [0, 3], 否], [[2], [], 是], [[0, 2], [], 是], [[1, 2], [0, 3], 否], [[0, 1, 2], [0, 3], 否], [[3], [1, 2], 否], [[0, 3], [1, 2], 否], [[1, 3], [0, 1, 2, 3], 是], [[0, 1, 3], [0, 1, 2, 3], 是], [[2, 3], [1, 2], 否], [[0, 2, 3], [1, 2], 否], [[1, 2, 3], [0, 1, 2, 3], 是], [[0, 1, 2, 3], [0, 1, 2, 3], 是]], 否, 否)；依完整明示資料重算；精確有限切片不自動升格為一般無限結論；逐一核目標可測集的逆像；可測不推出連續可積或保測。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限可測函數"]},"variant":{"family_id":"qf-mod24-measurable-composition-audit","seed":202610242100,"parameters":{"source_n":4,"middle_n":4,"target_n":4,"source_sigma":[[],[2],[0,1,3],[0,1,2,3]],"middle_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"target_sigma":[[],[0],[1],[0,1],[2],[0,2],[1,2],[0,1,2],[3],[0,3],[1,3],[0,1,3],[2,3],[0,2,3],[1,2,3],[0,1,2,3]],"first":[0,2,1,0],"second":[1,3,3,0],"domain":"Complete_finite_measurable_spaces","operation":"measurable-composition-audit","semantic_template":"qf-mod24-measurable-composition-audit/{\"first\":[0,2,1,0],\"middle_n\":4,\"middle_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]],\"second\":[1,3,3,0],\"source_n\":4,\"source_sigma\":[[],[0,1,2,3],[0,1,3],[2]],\"target_n\":4,\"target_sigma\":[[],[0,1,2,3],[0,1,2],[0,1,3],[0,1],[0,2,3],[0,2],[0,3],[0],[1,2,3],[1,2],[1,3],[1],[2,3],[2],[3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、Markov長期性、PDE適定性、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}