{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0001","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A=∅、B=∅，函數表為 ∅。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"是","explanation_zh":"單射=是；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053001,"parameters":{"A":[],"B":[],"pairs":[],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[],\"B\":[],\"operation\":\"bijective\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0002","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={0, 1}，函數表為 {(-1, 1), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"是","explanation_zh":"單射=是；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053002,"parameters":{"A":[-1,0],"B":[0,1],"pairs":[[-1,1],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-1,0],\"B\":[0,1],\"operation\":\"bijective\",\"pairs\":[[-1,1],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0003","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={1, 3, 5}，函數表為 {(-1, 1), (0, 3)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=是；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053003,"parameters":{"A":[-1,0],"B":[1,3,5],"pairs":[[-1,1],[0,3]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-1,0],\"B\":[1,3,5],\"operation\":\"bijective\",\"pairs\":[[-1,1],[0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0004","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={0}，函數表為 {(-1, 0), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053004,"parameters":{"A":[-1,0],"B":[0],"pairs":[[-1,0],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-1,0],\"B\":[0],\"operation\":\"bijective\",\"pairs\":[[-1,0],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0005","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={-3, -2, -1}，函數表為 {(-1, -1), (0, -1)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053005,"parameters":{"A":[-1,0],"B":[-3,-2,-1],"pairs":[[-1,-1],[0,-1]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-1,0],\"B\":[-3,-2,-1],\"operation\":\"bijective\",\"pairs\":[[-1,-1],[0,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0006","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={0, 1, 2}，函數表為 {(-2, 1), (-1, 2), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"是","explanation_zh":"單射=是；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053006,"parameters":{"A":[-2,-1,0],"B":[0,1,2],"pairs":[[-2,1],[-1,2],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-2,-1,0],\"B\":[0,1,2],\"operation\":\"bijective\",\"pairs\":[[-2,1],[-1,2],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0007","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={1, 3, 5, 7}，函數表為 {(-2, 1), (-1, 3), (0, 5)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=是；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053007,"parameters":{"A":[-2,-1,0],"B":[1,3,5,7],"pairs":[[-2,1],[-1,3],[0,5]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-2,-1,0],\"B\":[1,3,5,7],\"operation\":\"bijective\",\"pairs\":[[-2,1],[-1,3],[0,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0008","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={0, 1}，函數表為 {(-2, 0), (-1, 1), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053008,"parameters":{"A":[-2,-1,0],"B":[0,1],"pairs":[[-2,0],[-1,1],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-2,-1,0],\"B\":[0,1],\"operation\":\"bijective\",\"pairs\":[[-2,0],[-1,1],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0009","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={-4, -3, -2, -1}，函數表為 {(-2, -1), (-1, -1), (0, -2)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053009,"parameters":{"A":[-2,-1,0],"B":[-4,-3,-2,-1],"pairs":[[-2,-1],[-1,-1],[0,-2]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-2,-1,0],\"B\":[-4,-3,-2,-1],\"operation\":\"bijective\",\"pairs\":[[-2,-1],[-1,-1],[0,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0010","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={0, 1, 2, 3}，函數表為 {(-3, 1), (-2, 2), (-1, 3), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"是","explanation_zh":"單射=是；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053010,"parameters":{"A":[-3,-2,-1,0],"B":[0,1,2,3],"pairs":[[-3,1],[-2,2],[-1,3],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-3,-2,-1,0],\"B\":[0,1,2,3],\"operation\":\"bijective\",\"pairs\":[[-3,1],[-2,2],[-1,3],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0011","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={1, 3, 5, 7, 9}，函數表為 {(-3, 1), (-2, 3), (-1, 5), (0, 7)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=是；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053011,"parameters":{"A":[-3,-2,-1,0],"B":[1,3,5,7,9],"pairs":[[-3,1],[-2,3],[-1,5],[0,7]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-3,-2,-1,0],\"B\":[1,3,5,7,9],\"operation\":\"bijective\",\"pairs\":[[-3,1],[-2,3],[-1,5],[0,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0012","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={0, 1, 2}，函數表為 {(-3, 0), (-2, 1), (-1, 2), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053012,"parameters":{"A":[-3,-2,-1,0],"B":[0,1,2],"pairs":[[-3,0],[-2,1],[-1,2],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-3,-2,-1,0],\"B\":[0,1,2],\"operation\":\"bijective\",\"pairs\":[[-3,0],[-2,1],[-1,2],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0013","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={-5, -4, -3, -2, -1}，函數表為 {(-3, -1), (-2, -1), (-1, -2), (0, -2)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053013,"parameters":{"A":[-3,-2,-1,0],"B":[-5,-4,-3,-2,-1],"pairs":[[-3,-1],[-2,-1],[-1,-2],[0,-2]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-3,-2,-1,0],\"B\":[-5,-4,-3,-2,-1],\"operation\":\"bijective\",\"pairs\":[[-3,-1],[-2,-1],[-1,-2],[0,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0014","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4}，函數表為 {(-4, 1), (-3, 2), (-2, 3), (-1, 4), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"是","explanation_zh":"單射=是；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053014,"parameters":{"A":[-4,-3,-2,-1,0],"B":[0,1,2,3,4],"pairs":[[-4,1],[-3,2],[-2,3],[-1,4],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-4,-3,-2,-1,0],\"B\":[0,1,2,3,4],\"operation\":\"bijective\",\"pairs\":[[-4,1],[-3,2],[-2,3],[-1,4],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0015","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11}，函數表為 {(-4, 1), (-3, 3), (-2, 5), (-1, 7), (0, 9)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=是；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053015,"parameters":{"A":[-4,-3,-2,-1,0],"B":[1,3,5,7,9,11],"pairs":[[-4,1],[-3,3],[-2,5],[-1,7],[0,9]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-4,-3,-2,-1,0],\"B\":[1,3,5,7,9,11],\"operation\":\"bijective\",\"pairs\":[[-4,1],[-3,3],[-2,5],[-1,7],[0,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0016","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={0, 1, 2, 3}，函數表為 {(-4, 0), (-3, 1), (-2, 2), (-1, 3), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053016,"parameters":{"A":[-4,-3,-2,-1,0],"B":[0,1,2,3],"pairs":[[-4,0],[-3,1],[-2,2],[-1,3],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-4,-3,-2,-1,0],\"B\":[0,1,2,3],\"operation\":\"bijective\",\"pairs\":[[-4,0],[-3,1],[-2,2],[-1,3],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0017","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={-6, -5, -4, -3, -2, -1}，函數表為 {(-4, -1), (-3, -1), (-2, -2), (-1, -2), (0, -3)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053017,"parameters":{"A":[-4,-3,-2,-1,0],"B":[-6,-5,-4,-3,-2,-1],"pairs":[[-4,-1],[-3,-1],[-2,-2],[-1,-2],[0,-3]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-4,-3,-2,-1,0],\"B\":[-6,-5,-4,-3,-2,-1],\"operation\":\"bijective\",\"pairs\":[[-4,-1],[-3,-1],[-2,-2],[-1,-2],[0,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0018","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4, 5}，函數表為 {(-5, 1), (-4, 2), (-3, 3), (-2, 4), (-1, 5), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"是","explanation_zh":"單射=是；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053018,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4,5],"pairs":[[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4,5],\"operation\":\"bijective\",\"pairs\":[[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0019","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11, 13}，函數表為 {(-5, 1), (-4, 3), (-3, 5), (-2, 7), (-1, 9), (0, 11)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=是；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053019,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[1,3,5,7,9,11,13],"pairs":[[-5,1],[-4,3],[-3,5],[-2,7],[-1,9],[0,11]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[1,3,5,7,9,11,13],\"operation\":\"bijective\",\"pairs\":[[-5,1],[-4,3],[-3,5],[-2,7],[-1,9],[0,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0020","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4}，函數表為 {(-5, 0), (-4, 1), (-3, 2), (-2, 3), (-1, 4), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053020,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4],"pairs":[[-5,0],[-4,1],[-3,2],[-2,3],[-1,4],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4],\"operation\":\"bijective\",\"pairs\":[[-5,0],[-4,1],[-3,2],[-2,3],[-1,4],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0021","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={-7, -6, -5, -4, -3, -2, -1}，函數表為 {(-5, -1), (-4, -1), (-3, -2), (-2, -2), (-1, -3), (0, -3)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053021,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[-7,-6,-5,-4,-3,-2,-1],"pairs":[[-5,-1],[-4,-1],[-3,-2],[-2,-2],[-1,-3],[0,-3]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[-7,-6,-5,-4,-3,-2,-1],\"operation\":\"bijective\",\"pairs\":[[-5,-1],[-4,-1],[-3,-2],[-2,-2],[-1,-3],[0,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0022","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4, 5, 6}，函數表為 {(-6, 1), (-5, 2), (-4, 3), (-3, 4), (-2, 5), (-1, 6), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"是","explanation_zh":"單射=是；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053022,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4,5,6],"pairs":[[-6,1],[-5,2],[-4,3],[-3,4],[-2,5],[-1,6],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4,5,6],\"operation\":\"bijective\",\"pairs\":[[-6,1],[-5,2],[-4,3],[-3,4],[-2,5],[-1,6],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0023","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11, 13, 15}，函數表為 {(-6, 1), (-5, 3), (-4, 5), (-3, 7), (-2, 9), (-1, 11), (0, 13)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=是；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053023,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[1,3,5,7,9,11,13,15],"pairs":[[-6,1],[-5,3],[-4,5],[-3,7],[-2,9],[-1,11],[0,13]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[1,3,5,7,9,11,13,15],\"operation\":\"bijective\",\"pairs\":[[-6,1],[-5,3],[-4,5],[-3,7],[-2,9],[-1,11],[0,13]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0024","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4, 5}，函數表為 {(-6, 0), (-5, 1), (-4, 2), (-3, 3), (-2, 4), (-1, 5), (0, 0)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=是。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053024,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4,5],"pairs":[[-6,0],[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4,5],\"operation\":\"bijective\",\"pairs\":[[-6,0],[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0025","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限總函數的雙射性","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={-8, -7, -6, -5, -4, -3, -2, -1}，函數表為 {(-6, -1), (-5, -1), (-4, -2), (-3, -2), (-2, -3), (-1, -3), (0, -4)}。f 是否同時單射與滿射？請依實際表格判斷雙射性。","answer":{"kind":"short_text","value":"否","explanation_zh":"單射=否；滿射=否。兩個條件同時成立才是雙射；每個陪域目標必須恰有一個合法原像。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限總函數的雙射性"]},"variant":{"family_id":"qf-bijective-table-property","seed":202610053025,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[-8,-7,-6,-5,-4,-3,-2,-1],"pairs":[[-6,-1],[-5,-1],[-4,-2],[-3,-2],[-2,-3],[-1,-3],[0,-4]],"operation":"bijective","semantic_template":"qf-bijective-table-property/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[-8,-7,-6,-5,-4,-3,-2,-1],\"operation\":\"bijective\",\"pairs\":[[-6,-1],[-5,-1],[-4,-2],[-3,-2],[-2,-3],[-1,-3],[0,-4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0026","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A=∅、B=∅，函數表為 ∅。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"雙射","explanation_zh":"單射=是；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053026,"parameters":{"A":[],"B":[],"pairs":[],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[],\"B\":[],\"operation\":\"map_classification\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0027","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={0, 1}，函數表為 {(-1, 1), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"雙射","explanation_zh":"單射=是；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053027,"parameters":{"A":[-1,0],"B":[0,1],"pairs":[[-1,1],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-1,0],\"B\":[0,1],\"operation\":\"map_classification\",\"pairs\":[[-1,1],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0028","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={1, 3, 5}，函數表為 {(-1, 1), (0, 3)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅單射","explanation_zh":"單射=是；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053028,"parameters":{"A":[-1,0],"B":[1,3,5],"pairs":[[-1,1],[0,3]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-1,0],\"B\":[1,3,5],\"operation\":\"map_classification\",\"pairs\":[[-1,1],[0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0029","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={0}，函數表為 {(-1, 0), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅滿射","explanation_zh":"單射=否；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053029,"parameters":{"A":[-1,0],"B":[0],"pairs":[[-1,0],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-1,0],\"B\":[0],\"operation\":\"map_classification\",\"pairs\":[[-1,0],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0030","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={-3, -2, -1}，函數表為 {(-1, -1), (0, -1)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"既非單射也非滿射","explanation_zh":"單射=否；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053030,"parameters":{"A":[-1,0],"B":[-3,-2,-1],"pairs":[[-1,-1],[0,-1]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-1,0],\"B\":[-3,-2,-1],\"operation\":\"map_classification\",\"pairs\":[[-1,-1],[0,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0031","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={0, 1, 2}，函數表為 {(-2, 1), (-1, 2), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"雙射","explanation_zh":"單射=是；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053031,"parameters":{"A":[-2,-1,0],"B":[0,1,2],"pairs":[[-2,1],[-1,2],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-2,-1,0],\"B\":[0,1,2],\"operation\":\"map_classification\",\"pairs\":[[-2,1],[-1,2],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0032","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={1, 3, 5, 7}，函數表為 {(-2, 1), (-1, 3), (0, 5)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅單射","explanation_zh":"單射=是；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053032,"parameters":{"A":[-2,-1,0],"B":[1,3,5,7],"pairs":[[-2,1],[-1,3],[0,5]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-2,-1,0],\"B\":[1,3,5,7],\"operation\":\"map_classification\",\"pairs\":[[-2,1],[-1,3],[0,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0033","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={0, 1}，函數表為 {(-2, 0), (-1, 1), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅滿射","explanation_zh":"單射=否；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053033,"parameters":{"A":[-2,-1,0],"B":[0,1],"pairs":[[-2,0],[-1,1],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-2,-1,0],\"B\":[0,1],\"operation\":\"map_classification\",\"pairs\":[[-2,0],[-1,1],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0034","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={-4, -3, -2, -1}，函數表為 {(-2, -1), (-1, -1), (0, -2)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"既非單射也非滿射","explanation_zh":"單射=否；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053034,"parameters":{"A":[-2,-1,0],"B":[-4,-3,-2,-1],"pairs":[[-2,-1],[-1,-1],[0,-2]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-2,-1,0],\"B\":[-4,-3,-2,-1],\"operation\":\"map_classification\",\"pairs\":[[-2,-1],[-1,-1],[0,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0035","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={0, 1, 2, 3}，函數表為 {(-3, 1), (-2, 2), (-1, 3), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"雙射","explanation_zh":"單射=是；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053035,"parameters":{"A":[-3,-2,-1,0],"B":[0,1,2,3],"pairs":[[-3,1],[-2,2],[-1,3],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-3,-2,-1,0],\"B\":[0,1,2,3],\"operation\":\"map_classification\",\"pairs\":[[-3,1],[-2,2],[-1,3],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0036","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={1, 3, 5, 7, 9}，函數表為 {(-3, 1), (-2, 3), (-1, 5), (0, 7)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅單射","explanation_zh":"單射=是；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053036,"parameters":{"A":[-3,-2,-1,0],"B":[1,3,5,7,9],"pairs":[[-3,1],[-2,3],[-1,5],[0,7]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-3,-2,-1,0],\"B\":[1,3,5,7,9],\"operation\":\"map_classification\",\"pairs\":[[-3,1],[-2,3],[-1,5],[0,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0037","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={0, 1, 2}，函數表為 {(-3, 0), (-2, 1), (-1, 2), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅滿射","explanation_zh":"單射=否；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053037,"parameters":{"A":[-3,-2,-1,0],"B":[0,1,2],"pairs":[[-3,0],[-2,1],[-1,2],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-3,-2,-1,0],\"B\":[0,1,2],\"operation\":\"map_classification\",\"pairs\":[[-3,0],[-2,1],[-1,2],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0038","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={-5, -4, -3, -2, -1}，函數表為 {(-3, -1), (-2, -1), (-1, -2), (0, -2)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"既非單射也非滿射","explanation_zh":"單射=否；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053038,"parameters":{"A":[-3,-2,-1,0],"B":[-5,-4,-3,-2,-1],"pairs":[[-3,-1],[-2,-1],[-1,-2],[0,-2]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-3,-2,-1,0],\"B\":[-5,-4,-3,-2,-1],\"operation\":\"map_classification\",\"pairs\":[[-3,-1],[-2,-1],[-1,-2],[0,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0039","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4}，函數表為 {(-4, 1), (-3, 2), (-2, 3), (-1, 4), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"雙射","explanation_zh":"單射=是；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053039,"parameters":{"A":[-4,-3,-2,-1,0],"B":[0,1,2,3,4],"pairs":[[-4,1],[-3,2],[-2,3],[-1,4],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-4,-3,-2,-1,0],\"B\":[0,1,2,3,4],\"operation\":\"map_classification\",\"pairs\":[[-4,1],[-3,2],[-2,3],[-1,4],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0040","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11}，函數表為 {(-4, 1), (-3, 3), (-2, 5), (-1, 7), (0, 9)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅單射","explanation_zh":"單射=是；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053040,"parameters":{"A":[-4,-3,-2,-1,0],"B":[1,3,5,7,9,11],"pairs":[[-4,1],[-3,3],[-2,5],[-1,7],[0,9]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-4,-3,-2,-1,0],\"B\":[1,3,5,7,9,11],\"operation\":\"map_classification\",\"pairs\":[[-4,1],[-3,3],[-2,5],[-1,7],[0,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0041","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={0, 1, 2, 3}，函數表為 {(-4, 0), (-3, 1), (-2, 2), (-1, 3), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅滿射","explanation_zh":"單射=否；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053041,"parameters":{"A":[-4,-3,-2,-1,0],"B":[0,1,2,3],"pairs":[[-4,0],[-3,1],[-2,2],[-1,3],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-4,-3,-2,-1,0],\"B\":[0,1,2,3],\"operation\":\"map_classification\",\"pairs\":[[-4,0],[-3,1],[-2,2],[-1,3],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0042","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={-6, -5, -4, -3, -2, -1}，函數表為 {(-4, -1), (-3, -1), (-2, -2), (-1, -2), (0, -3)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"既非單射也非滿射","explanation_zh":"單射=否；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053042,"parameters":{"A":[-4,-3,-2,-1,0],"B":[-6,-5,-4,-3,-2,-1],"pairs":[[-4,-1],[-3,-1],[-2,-2],[-1,-2],[0,-3]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-4,-3,-2,-1,0],\"B\":[-6,-5,-4,-3,-2,-1],\"operation\":\"map_classification\",\"pairs\":[[-4,-1],[-3,-1],[-2,-2],[-1,-2],[0,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0043","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4, 5}，函數表為 {(-5, 1), (-4, 2), (-3, 3), (-2, 4), (-1, 5), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"雙射","explanation_zh":"單射=是；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053043,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4,5],"pairs":[[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4,5],\"operation\":\"map_classification\",\"pairs\":[[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0044","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11, 13}，函數表為 {(-5, 1), (-4, 3), (-3, 5), (-2, 7), (-1, 9), (0, 11)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅單射","explanation_zh":"單射=是；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053044,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[1,3,5,7,9,11,13],"pairs":[[-5,1],[-4,3],[-3,5],[-2,7],[-1,9],[0,11]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[1,3,5,7,9,11,13],\"operation\":\"map_classification\",\"pairs\":[[-5,1],[-4,3],[-3,5],[-2,7],[-1,9],[0,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0045","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4}，函數表為 {(-5, 0), (-4, 1), (-3, 2), (-2, 3), (-1, 4), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅滿射","explanation_zh":"單射=否；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053045,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4],"pairs":[[-5,0],[-4,1],[-3,2],[-2,3],[-1,4],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4],\"operation\":\"map_classification\",\"pairs\":[[-5,0],[-4,1],[-3,2],[-2,3],[-1,4],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0046","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={-7, -6, -5, -4, -3, -2, -1}，函數表為 {(-5, -1), (-4, -1), (-3, -2), (-2, -2), (-1, -3), (0, -3)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"既非單射也非滿射","explanation_zh":"單射=否；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053046,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[-7,-6,-5,-4,-3,-2,-1],"pairs":[[-5,-1],[-4,-1],[-3,-2],[-2,-2],[-1,-3],[0,-3]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[-7,-6,-5,-4,-3,-2,-1],\"operation\":\"map_classification\",\"pairs\":[[-5,-1],[-4,-1],[-3,-2],[-2,-2],[-1,-3],[0,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0047","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4, 5, 6}，函數表為 {(-6, 1), (-5, 2), (-4, 3), (-3, 4), (-2, 5), (-1, 6), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"雙射","explanation_zh":"單射=是；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053047,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4,5,6],"pairs":[[-6,1],[-5,2],[-4,3],[-3,4],[-2,5],[-1,6],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4,5,6],\"operation\":\"map_classification\",\"pairs\":[[-6,1],[-5,2],[-4,3],[-3,4],[-2,5],[-1,6],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0048","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11, 13, 15}，函數表為 {(-6, 1), (-5, 3), (-4, 5), (-3, 7), (-2, 9), (-1, 11), (0, 13)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅單射","explanation_zh":"單射=是；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053048,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[1,3,5,7,9,11,13,15],"pairs":[[-6,1],[-5,3],[-4,5],[-3,7],[-2,9],[-1,11],[0,13]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[1,3,5,7,9,11,13,15],\"operation\":\"map_classification\",\"pairs\":[[-6,1],[-5,3],[-4,5],[-3,7],[-2,9],[-1,11],[0,13]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0049","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4, 5}，函數表為 {(-6, 0), (-5, 1), (-4, 2), (-3, 3), (-2, 4), (-1, 5), (0, 0)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"僅滿射","explanation_zh":"單射=否；滿射=是。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053049,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4,5],"pairs":[[-6,0],[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4,5],\"operation\":\"map_classification\",\"pairs\":[[-6,0],[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0050","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"函數性質的四種分類","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={-8, -7, -6, -5, -4, -3, -2, -1}，函數表為 {(-6, -1), (-5, -1), (-4, -2), (-3, -2), (-2, -3), (-1, -3), (0, -4)}。分類為雙射、僅單射、僅滿射或既非單射也非滿射。","answer":{"kind":"short_text","value":"既非單射也非滿射","explanation_zh":"單射=否；滿射=否。依兩個性質的真假組合分類，不能只看定義域或陪域的元素個數。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["函數性質的四種分類"]},"variant":{"family_id":"qf-bijective-classification","seed":202610053050,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[-8,-7,-6,-5,-4,-3,-2,-1],"pairs":[[-6,-1],[-5,-1],[-4,-2],[-3,-2],[-2,-3],[-1,-3],[0,-4]],"operation":"map_classification","semantic_template":"qf-bijective-classification/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[-8,-7,-6,-5,-4,-3,-2,-1],\"operation\":\"map_classification\",\"pairs\":[[-6,-1],[-5,-1],[-4,-2],[-3,-2],[-2,-3],[-1,-3],[0,-4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0051","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A=∅、B=∅，函數表為 ∅。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"∅","explanation_zh":"纖維概況=∅。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053051,"parameters":{"A":[],"B":[],"pairs":[],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[],\"B\":[],\"operation\":\"fiber_profile\",\"pairs\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0052","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={0, 1}，函數表為 {(-1, 1), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 1), (1, 1)}","explanation_zh":"纖維概況={(0, 1), (1, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053052,"parameters":{"A":[-1,0],"B":[0,1],"pairs":[[-1,1],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-1,0],\"B\":[0,1],\"operation\":\"fiber_profile\",\"pairs\":[[-1,1],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0053","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={1, 3, 5}，函數表為 {(-1, 1), (0, 3)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(1, 1), (3, 1), (5, 0)}","explanation_zh":"纖維概況={(1, 1), (3, 1), (5, 0)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053053,"parameters":{"A":[-1,0],"B":[1,3,5],"pairs":[[-1,1],[0,3]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-1,0],\"B\":[1,3,5],\"operation\":\"fiber_profile\",\"pairs\":[[-1,1],[0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0054","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={0}，函數表為 {(-1, 0), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 2)}","explanation_zh":"纖維概況={(0, 2)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053054,"parameters":{"A":[-1,0],"B":[0],"pairs":[[-1,0],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-1,0],\"B\":[0],\"operation\":\"fiber_profile\",\"pairs\":[[-1,0],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0055","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-1, 0}、B={-3, -2, -1}，函數表為 {(-1, -1), (0, -1)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(-3, 0), (-2, 0), (-1, 2)}","explanation_zh":"纖維概況={(-3, 0), (-2, 0), (-1, 2)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053055,"parameters":{"A":[-1,0],"B":[-3,-2,-1],"pairs":[[-1,-1],[0,-1]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-1,0],\"B\":[-3,-2,-1],\"operation\":\"fiber_profile\",\"pairs\":[[-1,-1],[0,-1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0056","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={0, 1, 2}，函數表為 {(-2, 1), (-1, 2), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 1), (1, 1), (2, 1)}","explanation_zh":"纖維概況={(0, 1), (1, 1), (2, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053056,"parameters":{"A":[-2,-1,0],"B":[0,1,2],"pairs":[[-2,1],[-1,2],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-2,-1,0],\"B\":[0,1,2],\"operation\":\"fiber_profile\",\"pairs\":[[-2,1],[-1,2],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0057","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={1, 3, 5, 7}，函數表為 {(-2, 1), (-1, 3), (0, 5)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(1, 1), (3, 1), (5, 1), (7, 0)}","explanation_zh":"纖維概況={(1, 1), (3, 1), (5, 1), (7, 0)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053057,"parameters":{"A":[-2,-1,0],"B":[1,3,5,7],"pairs":[[-2,1],[-1,3],[0,5]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-2,-1,0],\"B\":[1,3,5,7],\"operation\":\"fiber_profile\",\"pairs\":[[-2,1],[-1,3],[0,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0058","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={0, 1}，函數表為 {(-2, 0), (-1, 1), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 2), (1, 1)}","explanation_zh":"纖維概況={(0, 2), (1, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053058,"parameters":{"A":[-2,-1,0],"B":[0,1],"pairs":[[-2,0],[-1,1],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-2,-1,0],\"B\":[0,1],\"operation\":\"fiber_profile\",\"pairs\":[[-2,0],[-1,1],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0059","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-2, -1, 0}、B={-4, -3, -2, -1}，函數表為 {(-2, -1), (-1, -1), (0, -2)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(-4, 0), (-3, 0), (-2, 1), (-1, 2)}","explanation_zh":"纖維概況={(-4, 0), (-3, 0), (-2, 1), (-1, 2)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053059,"parameters":{"A":[-2,-1,0],"B":[-4,-3,-2,-1],"pairs":[[-2,-1],[-1,-1],[0,-2]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-2,-1,0],\"B\":[-4,-3,-2,-1],\"operation\":\"fiber_profile\",\"pairs\":[[-2,-1],[-1,-1],[0,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0060","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={0, 1, 2, 3}，函數表為 {(-3, 1), (-2, 2), (-1, 3), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 1), (1, 1), (2, 1), (3, 1)}","explanation_zh":"纖維概況={(0, 1), (1, 1), (2, 1), (3, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053060,"parameters":{"A":[-3,-2,-1,0],"B":[0,1,2,3],"pairs":[[-3,1],[-2,2],[-1,3],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-3,-2,-1,0],\"B\":[0,1,2,3],\"operation\":\"fiber_profile\",\"pairs\":[[-3,1],[-2,2],[-1,3],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0061","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={1, 3, 5, 7, 9}，函數表為 {(-3, 1), (-2, 3), (-1, 5), (0, 7)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(1, 1), (3, 1), (5, 1), (7, 1), (9, 0)}","explanation_zh":"纖維概況={(1, 1), (3, 1), (5, 1), (7, 1), (9, 0)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053061,"parameters":{"A":[-3,-2,-1,0],"B":[1,3,5,7,9],"pairs":[[-3,1],[-2,3],[-1,5],[0,7]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-3,-2,-1,0],\"B\":[1,3,5,7,9],\"operation\":\"fiber_profile\",\"pairs\":[[-3,1],[-2,3],[-1,5],[0,7]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0062","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={0, 1, 2}，函數表為 {(-3, 0), (-2, 1), (-1, 2), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 2), (1, 1), (2, 1)}","explanation_zh":"纖維概況={(0, 2), (1, 1), (2, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053062,"parameters":{"A":[-3,-2,-1,0],"B":[0,1,2],"pairs":[[-3,0],[-2,1],[-1,2],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-3,-2,-1,0],\"B\":[0,1,2],\"operation\":\"fiber_profile\",\"pairs\":[[-3,0],[-2,1],[-1,2],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0063","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-3, -2, -1, 0}、B={-5, -4, -3, -2, -1}，函數表為 {(-3, -1), (-2, -1), (-1, -2), (0, -2)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(-5, 0), (-4, 0), (-3, 0), (-2, 2), (-1, 2)}","explanation_zh":"纖維概況={(-5, 0), (-4, 0), (-3, 0), (-2, 2), (-1, 2)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053063,"parameters":{"A":[-3,-2,-1,0],"B":[-5,-4,-3,-2,-1],"pairs":[[-3,-1],[-2,-1],[-1,-2],[0,-2]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-3,-2,-1,0],\"B\":[-5,-4,-3,-2,-1],\"operation\":\"fiber_profile\",\"pairs\":[[-3,-1],[-2,-1],[-1,-2],[0,-2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0064","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4}，函數表為 {(-4, 1), (-3, 2), (-2, 3), (-1, 4), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 1), (1, 1), (2, 1), (3, 1), (4, 1)}","explanation_zh":"纖維概況={(0, 1), (1, 1), (2, 1), (3, 1), (4, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053064,"parameters":{"A":[-4,-3,-2,-1,0],"B":[0,1,2,3,4],"pairs":[[-4,1],[-3,2],[-2,3],[-1,4],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-4,-3,-2,-1,0],\"B\":[0,1,2,3,4],\"operation\":\"fiber_profile\",\"pairs\":[[-4,1],[-3,2],[-2,3],[-1,4],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0065","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11}，函數表為 {(-4, 1), (-3, 3), (-2, 5), (-1, 7), (0, 9)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 0)}","explanation_zh":"纖維概況={(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 0)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053065,"parameters":{"A":[-4,-3,-2,-1,0],"B":[1,3,5,7,9,11],"pairs":[[-4,1],[-3,3],[-2,5],[-1,7],[0,9]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-4,-3,-2,-1,0],\"B\":[1,3,5,7,9,11],\"operation\":\"fiber_profile\",\"pairs\":[[-4,1],[-3,3],[-2,5],[-1,7],[0,9]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0066","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={0, 1, 2, 3}，函數表為 {(-4, 0), (-3, 1), (-2, 2), (-1, 3), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 2), (1, 1), (2, 1), (3, 1)}","explanation_zh":"纖維概況={(0, 2), (1, 1), (2, 1), (3, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053066,"parameters":{"A":[-4,-3,-2,-1,0],"B":[0,1,2,3],"pairs":[[-4,0],[-3,1],[-2,2],[-1,3],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-4,-3,-2,-1,0],\"B\":[0,1,2,3],\"operation\":\"fiber_profile\",\"pairs\":[[-4,0],[-3,1],[-2,2],[-1,3],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0067","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-4, -3, -2, -1, 0}、B={-6, -5, -4, -3, -2, -1}，函數表為 {(-4, -1), (-3, -1), (-2, -2), (-1, -2), (0, -3)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(-6, 0), (-5, 0), (-4, 0), (-3, 1), (-2, 2), (-1, 2)}","explanation_zh":"纖維概況={(-6, 0), (-5, 0), (-4, 0), (-3, 1), (-2, 2), (-1, 2)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053067,"parameters":{"A":[-4,-3,-2,-1,0],"B":[-6,-5,-4,-3,-2,-1],"pairs":[[-4,-1],[-3,-1],[-2,-2],[-1,-2],[0,-3]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-4,-3,-2,-1,0],\"B\":[-6,-5,-4,-3,-2,-1],\"operation\":\"fiber_profile\",\"pairs\":[[-4,-1],[-3,-1],[-2,-2],[-1,-2],[0,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0068","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4, 5}，函數表為 {(-5, 1), (-4, 2), (-3, 3), (-2, 4), (-1, 5), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1)}","explanation_zh":"纖維概況={(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053068,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4,5],"pairs":[[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4,5],\"operation\":\"fiber_profile\",\"pairs\":[[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0069","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11, 13}，函數表為 {(-5, 1), (-4, 3), (-3, 5), (-2, 7), (-1, 9), (0, 11)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 1), (13, 0)}","explanation_zh":"纖維概況={(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 1), (13, 0)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053069,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[1,3,5,7,9,11,13],"pairs":[[-5,1],[-4,3],[-3,5],[-2,7],[-1,9],[0,11]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[1,3,5,7,9,11,13],\"operation\":\"fiber_profile\",\"pairs\":[[-5,1],[-4,3],[-3,5],[-2,7],[-1,9],[0,11]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0070","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4}，函數表為 {(-5, 0), (-4, 1), (-3, 2), (-2, 3), (-1, 4), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 2), (1, 1), (2, 1), (3, 1), (4, 1)}","explanation_zh":"纖維概況={(0, 2), (1, 1), (2, 1), (3, 1), (4, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053070,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4],"pairs":[[-5,0],[-4,1],[-3,2],[-2,3],[-1,4],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4],\"operation\":\"fiber_profile\",\"pairs\":[[-5,0],[-4,1],[-3,2],[-2,3],[-1,4],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0071","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-5, -4, -3, -2, -1, 0}、B={-7, -6, -5, -4, -3, -2, -1}，函數表為 {(-5, -1), (-4, -1), (-3, -2), (-2, -2), (-1, -3), (0, -3)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(-7, 0), (-6, 0), (-5, 0), (-4, 0), (-3, 2), (-2, 2), (-1, 2)}","explanation_zh":"纖維概況={(-7, 0), (-6, 0), (-5, 0), (-4, 0), (-3, 2), (-2, 2), (-1, 2)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053071,"parameters":{"A":[-5,-4,-3,-2,-1,0],"B":[-7,-6,-5,-4,-3,-2,-1],"pairs":[[-5,-1],[-4,-1],[-3,-2],[-2,-2],[-1,-3],[0,-3]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-5,-4,-3,-2,-1,0],\"B\":[-7,-6,-5,-4,-3,-2,-1],\"operation\":\"fiber_profile\",\"pairs\":[[-5,-1],[-4,-1],[-3,-2],[-2,-2],[-1,-3],[0,-3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0072","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4, 5, 6}，函數表為 {(-6, 1), (-5, 2), (-4, 3), (-3, 4), (-2, 5), (-1, 6), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}","explanation_zh":"纖維概況={(0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053072,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4,5,6],"pairs":[[-6,1],[-5,2],[-4,3],[-3,4],[-2,5],[-1,6],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4,5,6],\"operation\":\"fiber_profile\",\"pairs\":[[-6,1],[-5,2],[-4,3],[-3,4],[-2,5],[-1,6],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0073","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11, 13, 15}，函數表為 {(-6, 1), (-5, 3), (-4, 5), (-3, 7), (-2, 9), (-1, 11), (0, 13)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 1), (13, 1), (15, 0)}","explanation_zh":"纖維概況={(1, 1), (3, 1), (5, 1), (7, 1), (9, 1), (11, 1), (13, 1), (15, 0)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053073,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[1,3,5,7,9,11,13,15],"pairs":[[-6,1],[-5,3],[-4,5],[-3,7],[-2,9],[-1,11],[0,13]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[1,3,5,7,9,11,13,15],\"operation\":\"fiber_profile\",\"pairs\":[[-6,1],[-5,3],[-4,5],[-3,7],[-2,9],[-1,11],[0,13]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0074","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={0, 1, 2, 3, 4, 5}，函數表為 {(-6, 0), (-5, 1), (-4, 2), (-3, 3), (-2, 4), (-1, 5), (0, 0)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(0, 2), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1)}","explanation_zh":"纖維概況={(0, 2), (1, 1), (2, 1), (3, 1), (4, 1), (5, 1)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053074,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[0,1,2,3,4,5],"pairs":[[-6,0],[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[0,1,2,3,4,5],\"operation\":\"fiber_profile\",\"pairs\":[[-6,0],[-5,1],[-4,2],[-3,3],[-2,4],[-1,5],[0,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0075","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"完整陪域纖維概況","stem_zh":"明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={-8, -7, -6, -5, -4, -3, -2, -1}，函數表為 {(-6, -1), (-5, -1), (-4, -2), (-3, -2), (-2, -3), (-1, -3), (0, -4)}。按目標數值順序列出全部 (b,|f⁻¹({b})|)，未命中的目標也須列零。","answer":{"kind":"short_text","value":"{(-8, 0), (-7, 0), (-6, 0), (-5, 0), (-4, 1), (-3, 2), (-2, 2), (-1, 2)}","explanation_zh":"纖維概況={(-8, 0), (-7, 0), (-6, 0), (-5, 0), (-4, 1), (-3, 2), (-2, 2), (-1, 2)}。每個 B 中目標都出現一次；概況包含零纖維，並非只把已命中的值列出。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整陪域纖維概況"]},"variant":{"family_id":"qf-bijective-fiber-profile","seed":202610053075,"parameters":{"A":[-6,-5,-4,-3,-2,-1,0],"B":[-8,-7,-6,-5,-4,-3,-2,-1],"pairs":[[-6,-1],[-5,-1],[-4,-2],[-3,-2],[-2,-3],[-1,-3],[0,-4]],"operation":"fiber_profile","semantic_template":"qf-bijective-fiber-profile/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B\":[-8,-7,-6,-5,-4,-3,-2,-1],\"operation\":\"fiber_profile\",\"pairs\":[[-6,-1],[-5,-1],[-4,-2],[-3,-2],[-2,-3],[-1,-3],[0,-4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0076","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=0、|B|=0，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"是","explanation_zh":"|A|=0；|B|=0。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053076,"parameters":{"a_size":0,"b_size":0,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":0,\"b_size\":0,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0077","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=0、|B|=1，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"否","explanation_zh":"|A|=0；|B|=1。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053077,"parameters":{"a_size":0,"b_size":1,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":0,\"b_size\":1,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0078","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=1、|B|=1，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"是","explanation_zh":"|A|=1；|B|=1。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053078,"parameters":{"a_size":1,"b_size":1,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":1,\"b_size\":1,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0079","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=1、|B|=2，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"否","explanation_zh":"|A|=1；|B|=2。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053079,"parameters":{"a_size":1,"b_size":2,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":1,\"b_size\":2,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0080","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=2、|B|=2，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"是","explanation_zh":"|A|=2；|B|=2。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053080,"parameters":{"a_size":2,"b_size":2,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":2,\"b_size\":2,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0081","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=2、|B|=3，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"否","explanation_zh":"|A|=2；|B|=3。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053081,"parameters":{"a_size":2,"b_size":3,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":2,\"b_size\":3,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0082","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=3、|B|=3，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"是","explanation_zh":"|A|=3；|B|=3。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053082,"parameters":{"a_size":3,"b_size":3,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":3,\"b_size\":3,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0083","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=3、|B|=4，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"否","explanation_zh":"|A|=3；|B|=4。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053083,"parameters":{"a_size":3,"b_size":4,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":3,\"b_size\":4,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0084","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=4、|B|=4，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"是","explanation_zh":"|A|=4；|B|=4。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053084,"parameters":{"a_size":4,"b_size":4,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":4,\"b_size\":4,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0085","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=4、|B|=5，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"否","explanation_zh":"|A|=4；|B|=5。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053085,"parameters":{"a_size":4,"b_size":5,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":4,\"b_size\":5,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0086","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=5、|B|=5，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"是","explanation_zh":"|A|=5；|B|=5。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053086,"parameters":{"a_size":5,"b_size":5,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":5,\"b_size\":5,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0087","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=5、|B|=6，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"否","explanation_zh":"|A|=5；|B|=6。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053087,"parameters":{"a_size":5,"b_size":6,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":5,\"b_size\":6,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0097","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=10、|B|=11，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"否","explanation_zh":"|A|=10；|B|=11。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053097,"parameters":{"a_size":10,"b_size":11,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":10,\"b_size\":11,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0098","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=11、|B|=11，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"是","explanation_zh":"|A|=11；|B|=11。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053098,"parameters":{"a_size":11,"b_size":11,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":11,\"b_size\":11,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0099","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=11、|B|=12，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"否","explanation_zh":"|A|=11；|B|=12。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053099,"parameters":{"a_size":11,"b_size":12,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":11,\"b_size\":12,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261004-advance-20261005-r03-bijective-0100","batch_id":"batch-20261004-advance-20261005-r03-bijective-foundations","language":"zh-Hant","source_mko_ids":["mko-bijective"],"title_zh":"有限基數下的雙射存在可能性","stem_zh":"明示有限基數 |A|=12、|B|=12，未提供任何特定函數表。是否存在某個 A→B 的雙射？","answer":{"kind":"short_text","value":"是","explanation_zh":"|A|=12；|B|=12。有限集合可逐一配對恰在基數相等時成立；這不是判斷給定函數，零到零也包含唯一空雙射。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限基數下的雙射存在可能性"]},"variant":{"family_id":"qf-bijective-cardinality-possibility","seed":202610053100,"parameters":{"a_size":12,"b_size":12,"operation":"cardinality_possibility","semantic_template":"qf-bijective-cardinality-possibility/{\"a_size\":12,\"b_size\":12,\"operation\":\"cardinality_possibility\"}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"Codex independent producer (inherited model; exact runtime model not exposed)","generated_at":"2026-10-04","contract_version":"ocme-question-factory-v0.1"}}