{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0001","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(0)→Fin(0)，索引從0；Fin(0)=∅，[]是空來源的完整表；images=[]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[]","explanation_zh":"完整函數圖形=[]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127001,"parameters":{"n":0,"m":0,"images":[],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0002","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(1)→Fin(1)，索引從0；images=[0]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 0]]","explanation_zh":"完整函數圖形=[[0, 0]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127002,"parameters":{"n":1,"m":1,"images":[0],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0003","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[2, 0, 5]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 2], [1, 0], [2, 5]]","explanation_zh":"完整函數圖形=[[0, 2], [1, 0], [2, 5]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127003,"parameters":{"n":3,"m":8,"images":[2,0,5],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[2,0,5]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0004","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[3, 0, 6]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 3], [1, 0], [2, 6]]","explanation_zh":"完整函數圖形=[[0, 3], [1, 0], [2, 6]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127004,"parameters":{"n":3,"m":8,"images":[3,0,6],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[3,0,6]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0005","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[4, 0, 7]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 4], [1, 0], [2, 7]]","explanation_zh":"完整函數圖形=[[0, 4], [1, 0], [2, 7]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127005,"parameters":{"n":3,"m":8,"images":[4,0,7],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[4,0,7]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0006","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[5, 0, 0]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 5], [1, 0], [2, 0]]","explanation_zh":"完整函數圖形=[[0, 5], [1, 0], [2, 0]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127006,"parameters":{"n":3,"m":8,"images":[5,0,0],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0007","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[6, 0, 1]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 6], [1, 0], [2, 1]]","explanation_zh":"完整函數圖形=[[0, 6], [1, 0], [2, 1]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127007,"parameters":{"n":3,"m":8,"images":[6,0,1],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[6,0,1]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0008","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[7, 0, 2]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 7], [1, 0], [2, 2]]","explanation_zh":"完整函數圖形=[[0, 7], [1, 0], [2, 2]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127008,"parameters":{"n":3,"m":8,"images":[7,0,2],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[7,0,2]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0009","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[0, 1, 3]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 0], [1, 1], [2, 3]]","explanation_zh":"完整函數圖形=[[0, 0], [1, 1], [2, 3]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127009,"parameters":{"n":3,"m":8,"images":[0,1,3],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[0,1,3]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0010","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[1, 1, 4]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 1], [1, 1], [2, 4]]","explanation_zh":"完整函數圖形=[[0, 1], [1, 1], [2, 4]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127010,"parameters":{"n":3,"m":8,"images":[1,1,4],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[1,1,4]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0011","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[2, 1, 5]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 2], [1, 1], [2, 5]]","explanation_zh":"完整函數圖形=[[0, 2], [1, 1], [2, 5]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127011,"parameters":{"n":3,"m":8,"images":[2,1,5],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[2,1,5]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0012","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[3, 1, 6]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 3], [1, 1], [2, 6]]","explanation_zh":"完整函數圖形=[[0, 3], [1, 1], [2, 6]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127012,"parameters":{"n":3,"m":8,"images":[3,1,6],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[3,1,6]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0013","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[4, 1, 7]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 4], [1, 1], [2, 7]]","explanation_zh":"完整函數圖形=[[0, 4], [1, 1], [2, 7]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127013,"parameters":{"n":3,"m":8,"images":[4,1,7],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[4,1,7]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0014","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[5, 1, 0]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 5], [1, 1], [2, 0]]","explanation_zh":"完整函數圖形=[[0, 5], [1, 1], [2, 0]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127014,"parameters":{"n":3,"m":8,"images":[5,1,0],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[5,1,0]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0015","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[6, 1, 1]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 6], [1, 1], [2, 1]]","explanation_zh":"完整函數圖形=[[0, 6], [1, 1], [2, 1]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127015,"parameters":{"n":3,"m":8,"images":[6,1,1],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[6,1,1]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0016","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[7, 1, 2]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 7], [1, 1], [2, 2]]","explanation_zh":"完整函數圖形=[[0, 7], [1, 1], [2, 2]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127016,"parameters":{"n":3,"m":8,"images":[7,1,2],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[7,1,2]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0017","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[0, 2, 3]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 0], [1, 2], [2, 3]]","explanation_zh":"完整函數圖形=[[0, 0], [1, 2], [2, 3]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127017,"parameters":{"n":3,"m":8,"images":[0,2,3],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[0,2,3]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0018","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[1, 2, 4]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 1], [1, 2], [2, 4]]","explanation_zh":"完整函數圖形=[[0, 1], [1, 2], [2, 4]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127018,"parameters":{"n":3,"m":8,"images":[1,2,4],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[1,2,4]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0019","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[2, 2, 5]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 2], [1, 2], [2, 5]]","explanation_zh":"完整函數圖形=[[0, 2], [1, 2], [2, 5]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127019,"parameters":{"n":3,"m":8,"images":[2,2,5],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[2,2,5]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0020","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[3, 2, 6]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 3], [1, 2], [2, 6]]","explanation_zh":"完整函數圖形=[[0, 3], [1, 2], [2, 6]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127020,"parameters":{"n":3,"m":8,"images":[3,2,6],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[3,2,6]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0021","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[4, 2, 7]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 4], [1, 2], [2, 7]]","explanation_zh":"完整函數圖形=[[0, 4], [1, 2], [2, 7]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127021,"parameters":{"n":3,"m":8,"images":[4,2,7],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[4,2,7]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0022","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[5, 2, 0]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 5], [1, 2], [2, 0]]","explanation_zh":"完整函數圖形=[[0, 5], [1, 2], [2, 0]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127022,"parameters":{"n":3,"m":8,"images":[5,2,0],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[5,2,0]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0023","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[6, 2, 1]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 6], [1, 2], [2, 1]]","explanation_zh":"完整函數圖形=[[0, 6], [1, 2], [2, 1]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127023,"parameters":{"n":3,"m":8,"images":[6,2,1],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[6,2,1]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0024","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[7, 2, 2]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 7], [1, 2], [2, 2]]","explanation_zh":"完整函數圖形=[[0, 7], [1, 2], [2, 2]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127024,"parameters":{"n":3,"m":8,"images":[7,2,2],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[7,2,2]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0025","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"完整有限函數圖形","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[0, 3, 3]。按來源索引列全部有序對[[i,f(i)],…]，空表列[]。","answer":{"kind":"expression","value":"[[0, 0], [1, 3], [2, 3]]","explanation_zh":"完整函數圖形=[[0, 0], [1, 3], [2, 3]]。完整讀每個合法輸入的唯一值，不按陪域補造圖形點；非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整有限函數圖形"]},"variant":{"family_id":"qf-density12-mapping-full-graph","seed":202610127025,"parameters":{"n":3,"m":8,"images":[0,3,3],"operation":"density12_mapping_full_graph","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-full-graph/[0,3,3]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0026","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"值域與未用陪域","stem_zh":"完整有限總映射 f:Fin(0)→Fin(0)，索引從0；Fin(0)=∅，[]是空來源的完整表；images=[]。依序列 (遞增實際值域, 遞增未使用的Fin(m)陪域元素, 值域是否等於整個陪域)。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"值域與未用陪域=([], [], 是)。先去重所有輸出，再枚舉陪域未用項；全定義不保證滿射，非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["值域與未用陪域"]},"variant":{"family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127026,"parameters":{"n":0,"m":0,"images":[],"operation":"density12_mapping_range_codomain_defect","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-range-codomain-defect/[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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0032","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"值域與未用陪域","stem_zh":"完整有限總映射 f:Fin(1)→Fin(8)，索引從0；images=[2]。依序列 (遞增實際值域, 遞增未使用的Fin(m)陪域元素, 值域是否等於整個陪域)。","answer":{"kind":"expression","value":"([2], [0, 1, 3, 4, 5, 6, 7], 否)","explanation_zh":"值域與未用陪域=([2], [0, 1, 3, 4, 5, 6, 7], 否)。先去重所有輸出，再枚舉陪域未用項；全定義不保證滿射，非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["值域與未用陪域"]},"variant":{"family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127032,"parameters":{"n":1,"m":8,"images":[2],"operation":"density12_mapping_range_codomain_defect","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0046","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"值域與未用陪域","stem_zh":"完整有限總映射 f:Fin(2)→Fin(8)，索引從0；images=[1, 4]。依序列 (遞增實際值域, 遞增未使用的Fin(m)陪域元素, 值域是否等於整個陪域)。","answer":{"kind":"expression","value":"([1, 4], [0, 2, 3, 5, 6, 7], 否)","explanation_zh":"值域與未用陪域=([1, 4], [0, 2, 3, 5, 6, 7], 否)。先去重所有輸出，再枚舉陪域未用項；全定義不保證滿射，非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["值域與未用陪域"]},"variant":{"family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127046,"parameters":{"n":2,"m":8,"images":[1,4],"operation":"density12_mapping_range_codomain_defect","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[1,4]]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261008-advance-20261012-r07-function-mapping-0049","batch_id":"batch-20261008-advance-20261012-r07-function-mapping-foundations","language":"zh-Hant","source_mko_ids":["mko-function-mapping"],"title_zh":"值域與未用陪域","stem_zh":"完整有限總映射 f:Fin(3)→Fin(8)，索引從0；images=[0, 2, 4]。依序列 (遞增實際值域, 遞增未使用的Fin(m)陪域元素, 值域是否等於整個陪域)。","answer":{"kind":"expression","value":"([0, 2, 4], [1, 3, 5, 6, 7], 否)","explanation_zh":"值域與未用陪域=([0, 2, 4], [1, 3, 5, 6, 7], 否)。先去重所有輸出，再枚舉陪域未用項；全定義不保證滿射，非部分程式函數。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["值域與未用陪域"]},"variant":{"family_id":"qf-density12-mapping-range-codomain-defect","seed":202610127049,"parameters":{"n":3,"m":8,"images":[0,2,4],"operation":"density12_mapping_range_codomain_defect","domain":"finite_total_mapping_protocol","semantic_template":"qf-density12-mapping-range-codomain-defect/[8,[0,2,4]]"}},"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":"model_unknown","generated_at":"2026-10-08","contract_version":"ocme-question-factory-v0.1"}}
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