{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0001","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(0)=∅，Fin(0)=∅。完整合型images[x]表=[]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([0, 0], [], [], [], 0)","explanation_zh":"定義陪域完整圖與值域=([0, 0], [], [], [], 0)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153001,"parameters":{"n":0,"m":0,"images":[],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0002","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[0, 0, 0]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 0], [2, 0]], [0], [1, 2], 1)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 0], [1, 0], [2, 0]], [0], [1, 2], 1)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153002,"parameters":{"n":3,"m":3,"images":[0,0,0],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0003","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[1, 0, 0]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 0], [2, 0]], [0, 1], [2], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 1], [1, 0], [2, 0]], [0, 1], [2], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153003,"parameters":{"n":3,"m":3,"images":[1,0,0],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0004","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[2, 0, 0]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 0], [2, 0]], [0, 2], [1], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 2], [1, 0], [2, 0]], [0, 2], [1], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153004,"parameters":{"n":3,"m":3,"images":[2,0,0],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0005","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[0, 1, 0]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 1], [2, 0]], [0, 1], [2], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 0], [1, 1], [2, 0]], [0, 1], [2], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153005,"parameters":{"n":3,"m":3,"images":[0,1,0],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,1,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0006","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[1, 1, 0]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 1], [2, 0]], [0, 1], [2], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 1], [1, 1], [2, 0]], [0, 1], [2], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153006,"parameters":{"n":3,"m":3,"images":[1,1,0],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,1,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0007","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[2, 1, 0]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 1], [2, 0]], [0, 1, 2], [], 3)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 2], [1, 1], [2, 0]], [0, 1, 2], [], 3)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153007,"parameters":{"n":3,"m":3,"images":[2,1,0],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,1,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0008","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[0, 2, 0]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 2], [2, 0]], [0, 2], [1], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 0], [1, 2], [2, 0]], [0, 2], [1], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153008,"parameters":{"n":3,"m":3,"images":[0,2,0],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,2,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0009","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[1, 2, 0]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 2], [2, 0]], [0, 1, 2], [], 3)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 1], [1, 2], [2, 0]], [0, 1, 2], [], 3)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153009,"parameters":{"n":3,"m":3,"images":[1,2,0],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,2,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0010","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[2, 2, 0]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 2], [2, 0]], [0, 2], [1], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 2], [1, 2], [2, 0]], [0, 2], [1], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153010,"parameters":{"n":3,"m":3,"images":[2,2,0],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,2,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0011","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[0, 0, 1]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 0], [2, 1]], [0, 1], [2], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 0], [1, 0], [2, 1]], [0, 1], [2], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153011,"parameters":{"n":3,"m":3,"images":[0,0,1],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,0,1]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0012","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[1, 0, 1]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 0], [2, 1]], [0, 1], [2], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 1], [1, 0], [2, 1]], [0, 1], [2], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153012,"parameters":{"n":3,"m":3,"images":[1,0,1],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0013","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[2, 0, 1]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 0], [2, 1]], [0, 1, 2], [], 3)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 2], [1, 0], [2, 1]], [0, 1, 2], [], 3)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153013,"parameters":{"n":3,"m":3,"images":[2,0,1],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,0,1]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0014","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[0, 1, 1]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 1], [2, 1]], [0, 1], [2], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 0], [1, 1], [2, 1]], [0, 1], [2], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153014,"parameters":{"n":3,"m":3,"images":[0,1,1],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,1,1]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0015","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[1, 1, 1]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 1], [2, 1]], [1], [0, 2], 1)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 1], [1, 1], [2, 1]], [1], [0, 2], 1)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153015,"parameters":{"n":3,"m":3,"images":[1,1,1],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,1,1]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0016","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[2, 1, 1]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 1], [2, 1]], [1, 2], [0], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 2], [1, 1], [2, 1]], [1, 2], [0], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153016,"parameters":{"n":3,"m":3,"images":[2,1,1],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,1,1]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0017","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[0, 2, 1]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 2], [2, 1]], [0, 1, 2], [], 3)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 0], [1, 2], [2, 1]], [0, 1, 2], [], 3)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153017,"parameters":{"n":3,"m":3,"images":[0,2,1],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,2,1]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0018","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[1, 2, 1]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 2], [2, 1]], [1, 2], [0], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 1], [1, 2], [2, 1]], [1, 2], [0], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153018,"parameters":{"n":3,"m":3,"images":[1,2,1],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,2,1]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0019","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[2, 2, 1]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 2], [2, 1]], [1, 2], [0], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 2], [1, 2], [2, 1]], [1, 2], [0], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153019,"parameters":{"n":3,"m":3,"images":[2,2,1],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,2,1]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0020","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[0, 0, 2]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 0], [2, 2]], [0, 2], [1], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 0], [1, 0], [2, 2]], [0, 2], [1], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153020,"parameters":{"n":3,"m":3,"images":[0,0,2],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,0,2]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0021","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[1, 0, 2]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 0], [2, 2]], [0, 1, 2], [], 3)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 1], [1, 0], [2, 2]], [0, 1, 2], [], 3)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153021,"parameters":{"n":3,"m":3,"images":[1,0,2],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0022","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[2, 0, 2]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 0], [2, 2]], [0, 2], [1], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 2], [1, 0], [2, 2]], [0, 2], [1], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153022,"parameters":{"n":3,"m":3,"images":[2,0,2],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0023","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[0, 1, 2]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 0], [1, 1], [2, 2]], [0, 1, 2], [], 3)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 0], [1, 1], [2, 2]], [0, 1, 2], [], 3)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153023,"parameters":{"n":3,"m":3,"images":[0,1,2],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[0,1,2]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0024","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[1, 1, 2]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 1], [1, 1], [2, 2]], [1, 2], [0], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 1], [1, 1], [2, 2]], [1, 2], [0], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153024,"parameters":{"n":3,"m":3,"images":[1,1,2],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[1,1,2]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0025","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"完整型別表與值域清單","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(3)=[0, 1, 2]。完整合型images[x]表=[2, 1, 2]。求 ([n,m], 全部[x,images[x]]列, 值域, 未用陪域, 值域大小)。","answer":{"kind":"expression","value":"([3, 3], [[0, 2], [1, 1], [2, 2]], [1, 2], [0], 2)","explanation_zh":"定義陪域完整圖與值域=([3, 3], [[0, 2], [1, 1], [2, 2]], [1, 2], [0], 2)。逐輸入列圖，重複輸出去重為值域，再從陪域扣除。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["完整型別表與值域清單"]},"variant":{"family_id":"qf-density15-typed-domain-range-inventory","seed":202610153025,"parameters":{"n":3,"m":3,"images":[2,1,2],"domain":"finite_typed_function_data","operation":"density15_typed_domain_range_inventory","semantic_template":"qf-density15-typed-domain-range-inventory/[3,3,[2,1,2]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0026","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(0)=∅，Fin(0)=∅。完整合型images表=[]，有序陪域候選=[0, -1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([否, 否], [不合陪域, 不合陪域], [不合陪域, 不合陪域])","explanation_zh":"陪域候選資格與原像列=([否, 否], [不合陪域, 不合陪域], [不合陪域, 不合陪域])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153026,"parameters":{"n":0,"m":0,"images":[],"queries":[0,-1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"untyped\"],[\"untyped\"]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0027","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(0)=∅，Fin(2)=[0, 1]。完整合型images表=[]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[], []], [0, 0])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[], []], [0, 0])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153027,"parameters":{"n":0,"m":2,"images":[],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[]],[\"typed\",[]]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0028","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。完整合型images表=[0, 1, 0]，有序陪域候選=[2, 0]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([否, 是], [不合陪域, [0, 2]], [不合陪域, 2])","explanation_zh":"陪域候選資格與原像列=([否, 是], [不合陪域, [0, 2]], [不合陪域, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153028,"parameters":{"n":3,"m":2,"images":[0,1,0],"queries":[2,0],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"untyped\"],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0029","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 0, 0, 0, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 1, 2, 3, 4], []], [5, 0])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 1, 2, 3, 4], []], [5, 0])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153029,"parameters":{"n":5,"m":3,"images":[0,0,0,0,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,2,3,4]],[\"typed\",[]]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0030","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 0, 0, 0, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[1, 2, 3, 4], [0]], [4, 1])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[1, 2, 3, 4], [0]], [4, 1])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153030,"parameters":{"n":5,"m":3,"images":[1,0,0,0,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,2,3,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0031","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 1, 0, 0, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 2, 3, 4], [1]], [4, 1])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 2, 3, 4], [1]], [4, 1])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153031,"parameters":{"n":5,"m":3,"images":[0,1,0,0,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,2,3,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0032","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 1, 0, 0, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[2, 3, 4], [0, 1]], [3, 2])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[2, 3, 4], [0, 1]], [3, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153032,"parameters":{"n":5,"m":3,"images":[1,1,0,0,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[2,3,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0033","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 0, 1, 0, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 1, 3, 4], [2]], [4, 1])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 1, 3, 4], [2]], [4, 1])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153033,"parameters":{"n":5,"m":3,"images":[0,0,1,0,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,3,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0034","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 0, 1, 0, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[1, 3, 4], [0, 2]], [3, 2])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[1, 3, 4], [0, 2]], [3, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153034,"parameters":{"n":5,"m":3,"images":[1,0,1,0,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,3,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0035","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 1, 1, 0, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 3, 4], [1, 2]], [3, 2])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 3, 4], [1, 2]], [3, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153035,"parameters":{"n":5,"m":3,"images":[0,1,1,0,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,3,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0036","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 1, 1, 0, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[3, 4], [0, 1, 2]], [2, 3])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[3, 4], [0, 1, 2]], [2, 3])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153036,"parameters":{"n":5,"m":3,"images":[1,1,1,0,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[3,4]],[\"typed\",[0,1,2]]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0037","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 0, 0, 1, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 1, 2, 4], [3]], [4, 1])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 1, 2, 4], [3]], [4, 1])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153037,"parameters":{"n":5,"m":3,"images":[0,0,0,1,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,2,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0038","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 0, 0, 1, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[1, 2, 4], [0, 3]], [3, 2])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[1, 2, 4], [0, 3]], [3, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153038,"parameters":{"n":5,"m":3,"images":[1,0,0,1,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,2,4]],[\"typed\",[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0039","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 1, 0, 1, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 2, 4], [1, 3]], [3, 2])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 2, 4], [1, 3]], [3, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153039,"parameters":{"n":5,"m":3,"images":[0,1,0,1,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,2,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0040","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 1, 0, 1, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[2, 4], [0, 1, 3]], [2, 3])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[2, 4], [0, 1, 3]], [2, 3])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153040,"parameters":{"n":5,"m":3,"images":[1,1,0,1,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[2,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0041","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 0, 1, 1, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 1, 4], [2, 3]], [3, 2])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 1, 4], [2, 3]], [3, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153041,"parameters":{"n":5,"m":3,"images":[0,0,1,1,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0042","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 0, 1, 1, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[1, 4], [0, 2, 3]], [2, 3])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[1, 4], [0, 2, 3]], [2, 3])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153042,"parameters":{"n":5,"m":3,"images":[1,0,1,1,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,4]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0043","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 1, 1, 1, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 4], [1, 2, 3]], [2, 3])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 4], [1, 2, 3]], [2, 3])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153043,"parameters":{"n":5,"m":3,"images":[0,1,1,1,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,4]],[\"typed\",[1,2,3]]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0044","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 1, 1, 1, 0]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[4], [0, 1, 2, 3]], [1, 4])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[4], [0, 1, 2, 3]], [1, 4])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153044,"parameters":{"n":5,"m":3,"images":[1,1,1,1,0],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[4]],[\"typed\",[0,1,2,3]]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0045","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 0, 0, 0, 1]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 1, 2, 3], [4]], [4, 1])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 1, 2, 3], [4]], [4, 1])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153045,"parameters":{"n":5,"m":3,"images":[0,0,0,0,1],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,2,3]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0046","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 0, 0, 0, 1]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[1, 2, 3], [0, 4]], [3, 2])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[1, 2, 3], [0, 4]], [3, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153046,"parameters":{"n":5,"m":3,"images":[1,0,0,0,1],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,2,3]],[\"typed\",[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0047","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 1, 0, 0, 1]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 2, 3], [1, 4]], [3, 2])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 2, 3], [1, 4]], [3, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153047,"parameters":{"n":5,"m":3,"images":[0,1,0,0,1],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,2,3]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0048","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 1, 0, 0, 1]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[2, 3], [0, 1, 4]], [2, 3])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[2, 3], [0, 1, 4]], [2, 3])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153048,"parameters":{"n":5,"m":3,"images":[1,1,0,0,1],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[2,3]],[\"typed\",[0,1,4]]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0049","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[0, 0, 1, 0, 1]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[0, 1, 3], [2, 4]], [3, 2])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[0, 1, 3], [2, 4]], [3, 2])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153049,"parameters":{"n":5,"m":3,"images":[0,0,1,0,1],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[0,1,3]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0050","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"陪域候選與完整原像","stem_zh":"Fin型別從0起，Fin(5)=[0, 1, 2, 3, 4]，Fin(3)=[0, 1, 2]。完整合型images表=[1, 0, 1, 0, 1]，有序陪域候選=[0, 1]。求 (候選型別資格, 各原像索引列或不合陪域, 各大小或不合陪域)。域外候選不作合法空原像。","answer":{"kind":"expression","value":"([是, 是], [[1, 3], [0, 2, 4]], [2, 3])","explanation_zh":"陪域候選資格與原像列=([是, 是], [[1, 3], [0, 2, 4]], [2, 3])。先核候選是否屬陪域；合型才遍歷全部來源列找輸出相等的位置。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["陪域候選與完整原像"]},"variant":{"family_id":"qf-density15-typed-mapping-preimage-two-values","seed":202610153050,"parameters":{"n":5,"m":3,"images":[1,0,1,0,1],"queries":[0,1],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_preimage_two_values","semantic_template":"qf-density15-typed-mapping-preimage-two-values/[[\"typed\",[1,3]],[\"typed\",[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0051","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(1)=[0]，Fin(1)=[0]。原完整合型images=[0]，at=0，新value=0。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(0, [0], [0], [], [], 1)","explanation_zh":"替換映射表與值域增刪=(0, [0], [0], [], [], 1)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153051,"parameters":{"n":1,"m":1,"images":[0],"at":0,"value":0,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0052","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(2)=[0, 1]，Fin(2)=[0, 1]。原完整合型images=[0, 1]，at=0，新value=1。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(0, [1, 1], [1], [0], [], 2)","explanation_zh":"替換映射表與值域增刪=(0, [1, 1], [1], [0], [], 2)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153052,"parameters":{"n":2,"m":2,"images":[0,1],"at":0,"value":1,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[1,1],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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0053","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(2)=[0, 1]，Fin(3)=[0, 1, 2]。原完整合型images=[0, 0]，at=0，新value=2。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(0, [2, 0], [0, 2], [], [2], 3)","explanation_zh":"替換映射表與值域增刪=(0, [2, 0], [0, 2], [], [2], 3)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153053,"parameters":{"n":2,"m":3,"images":[0,0],"at":0,"value":2,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[2,0],3,[],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0054","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(2)=[0, 1]，Fin(2)=[0, 1]。原完整合型images=[0, 1]，at=1，新value=1。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(1, [0, 1], [0, 1], [], [], 2)","explanation_zh":"替換映射表與值域增刪=(1, [0, 1], [0, 1], [], [], 2)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153054,"parameters":{"n":2,"m":2,"images":[0,1],"at":1,"value":1,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[1,[0,1],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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0055","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[4, 0, 5]，at=0，新value=7。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(4, [7, 0, 5], [0, 5, 7], [4], [7], 8)","explanation_zh":"替換映射表與值域增刪=(4, [7, 0, 5], [0, 5, 7], [4], [7], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153055,"parameters":{"n":3,"m":8,"images":[4,0,5],"at":0,"value":7,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[4,[7,0,5],8,[4],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0056","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[5, 0, 6]，at=0，新value=0。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(5, [0, 0, 6], [0, 6], [5], [], 8)","explanation_zh":"替換映射表與值域增刪=(5, [0, 0, 6], [0, 6], [5], [], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153056,"parameters":{"n":3,"m":8,"images":[5,0,6],"at":0,"value":0,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[5,[0,0,6],8,[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0057","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[6, 0, 7]，at=0，新value=1。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(6, [1, 0, 7], [0, 1, 7], [6], [1], 8)","explanation_zh":"替換映射表與值域增刪=(6, [1, 0, 7], [0, 1, 7], [6], [1], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153057,"parameters":{"n":3,"m":8,"images":[6,0,7],"at":0,"value":1,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[6,[1,0,7],8,[6],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0058","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[7, 0, 0]，at=0，新value=2。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(7, [2, 0, 0], [0, 2], [7], [2], 8)","explanation_zh":"替換映射表與值域增刪=(7, [2, 0, 0], [0, 2], [7], [2], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153058,"parameters":{"n":3,"m":8,"images":[7,0,0],"at":0,"value":2,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[7,[2,0,0],8,[7],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0059","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[0, 1, 1]，at=0，新value=3。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(0, [3, 1, 1], [1, 3], [0], [3], 8)","explanation_zh":"替換映射表與值域增刪=(0, [3, 1, 1], [1, 3], [0], [3], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153059,"parameters":{"n":3,"m":8,"images":[0,1,1],"at":0,"value":3,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[3,1,1],8,[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0060","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[1, 1, 2]，at=0，新value=4。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(1, [4, 1, 2], [1, 2, 4], [], [4], 8)","explanation_zh":"替換映射表與值域增刪=(1, [4, 1, 2], [1, 2, 4], [], [4], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153060,"parameters":{"n":3,"m":8,"images":[1,1,2],"at":0,"value":4,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[1,[4,1,2],8,[],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0061","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[2, 1, 3]，at=0，新value=5。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(2, [5, 1, 3], [1, 3, 5], [2], [5], 8)","explanation_zh":"替換映射表與值域增刪=(2, [5, 1, 3], [1, 3, 5], [2], [5], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153061,"parameters":{"n":3,"m":8,"images":[2,1,3],"at":0,"value":5,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[2,[5,1,3],8,[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0062","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[3, 1, 4]，at=0，新value=6。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(3, [6, 1, 4], [1, 4, 6], [3], [6], 8)","explanation_zh":"替換映射表與值域增刪=(3, [6, 1, 4], [1, 4, 6], [3], [6], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153062,"parameters":{"n":3,"m":8,"images":[3,1,4],"at":0,"value":6,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[3,[6,1,4],8,[3],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0063","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[4, 1, 5]，at=0，新value=7。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(4, [7, 1, 5], [1, 5, 7], [4], [7], 8)","explanation_zh":"替換映射表與值域增刪=(4, [7, 1, 5], [1, 5, 7], [4], [7], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153063,"parameters":{"n":3,"m":8,"images":[4,1,5],"at":0,"value":7,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[4,[7,1,5],8,[4],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0064","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[5, 1, 6]，at=0，新value=0。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(5, [0, 1, 6], [0, 1, 6], [5], [0], 8)","explanation_zh":"替換映射表與值域增刪=(5, [0, 1, 6], [0, 1, 6], [5], [0], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153064,"parameters":{"n":3,"m":8,"images":[5,1,6],"at":0,"value":0,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[5,[0,1,6],8,[5],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0065","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[6, 1, 7]，at=0，新value=1。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(6, [1, 1, 7], [1, 7], [6], [], 8)","explanation_zh":"替換映射表與值域增刪=(6, [1, 1, 7], [1, 7], [6], [], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153065,"parameters":{"n":3,"m":8,"images":[6,1,7],"at":0,"value":1,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[6,[1,1,7],8,[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0066","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[7, 1, 0]，at=0，新value=2。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(7, [2, 1, 0], [0, 1, 2], [7], [2], 8)","explanation_zh":"替換映射表與值域增刪=(7, [2, 1, 0], [0, 1, 2], [7], [2], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153066,"parameters":{"n":3,"m":8,"images":[7,1,0],"at":0,"value":2,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[7,[2,1,0],8,[7],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0067","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[0, 2, 1]，at=0，新value=3。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(0, [3, 2, 1], [1, 2, 3], [0], [3], 8)","explanation_zh":"替換映射表與值域增刪=(0, [3, 2, 1], [1, 2, 3], [0], [3], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153067,"parameters":{"n":3,"m":8,"images":[0,2,1],"at":0,"value":3,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[3,2,1],8,[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":"model_unknown","generated_at":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0068","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[1, 2, 2]，at=0，新value=4。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(1, [4, 2, 2], [2, 4], [1], [4], 8)","explanation_zh":"替換映射表與值域增刪=(1, [4, 2, 2], [2, 4], [1], [4], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153068,"parameters":{"n":3,"m":8,"images":[1,2,2],"at":0,"value":4,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[1,[4,2,2],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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0069","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[2, 2, 3]，at=0，新value=5。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(2, [5, 2, 3], [2, 3, 5], [], [5], 8)","explanation_zh":"替換映射表與值域增刪=(2, [5, 2, 3], [2, 3, 5], [], [5], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153069,"parameters":{"n":3,"m":8,"images":[2,2,3],"at":0,"value":5,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[2,[5,2,3],8,[],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0070","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[3, 2, 4]，at=0，新value=6。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(3, [6, 2, 4], [2, 4, 6], [3], [6], 8)","explanation_zh":"替換映射表與值域增刪=(3, [6, 2, 4], [2, 4, 6], [3], [6], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153070,"parameters":{"n":3,"m":8,"images":[3,2,4],"at":0,"value":6,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[3,[6,2,4],8,[3],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0071","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[4, 2, 5]，at=0，新value=7。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(4, [7, 2, 5], [2, 5, 7], [4], [7], 8)","explanation_zh":"替換映射表與值域增刪=(4, [7, 2, 5], [2, 5, 7], [4], [7], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153071,"parameters":{"n":3,"m":8,"images":[4,2,5],"at":0,"value":7,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[4,[7,2,5],8,[4],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0072","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[5, 2, 6]，at=0，新value=0。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(5, [0, 2, 6], [0, 2, 6], [5], [0], 8)","explanation_zh":"替換映射表與值域增刪=(5, [0, 2, 6], [0, 2, 6], [5], [0], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153072,"parameters":{"n":3,"m":8,"images":[5,2,6],"at":0,"value":0,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[5,[0,2,6],8,[5],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0073","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[6, 2, 7]，at=0，新value=1。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(6, [1, 2, 7], [1, 2, 7], [6], [1], 8)","explanation_zh":"替換映射表與值域增刪=(6, [1, 2, 7], [1, 2, 7], [6], [1], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153073,"parameters":{"n":3,"m":8,"images":[6,2,7],"at":0,"value":1,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[6,[1,2,7],8,[6],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0074","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[7, 2, 0]，at=0，新value=2。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(7, [2, 2, 0], [0, 2], [7], [], 8)","explanation_zh":"替換映射表與值域增刪=(7, [2, 2, 0], [0, 2], [7], [], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153074,"parameters":{"n":3,"m":8,"images":[7,2,0],"at":0,"value":2,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[7,[2,2,0],8,[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0075","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"單格替換與值域增刪","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]。原完整合型images=[0, 3, 1]，at=0，新value=3。原表全格先合法，再作替換。求 (舊值, 新表, 新值域, 消失值, 新增值, m)。","answer":{"kind":"expression","value":"(0, [3, 3, 1], [1, 3], [0], [], 8)","explanation_zh":"替換映射表與值域增刪=(0, [3, 3, 1], [1, 3], [0], [], 8)。保留其餘表格列；新舊值域分別列集合差，同值替換不造新增值。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["單格替換與值域增刪"]},"variant":{"family_id":"qf-density15-typed-mapping-output-replacement","seed":202610153075,"parameters":{"n":3,"m":8,"images":[0,3,1],"at":0,"value":3,"domain":"finite_typed_function_data","operation":"density15_typed_mapping_output_replacement","semantic_template":"qf-density15-typed-mapping-output-replacement/[0,[3,3,1],8,[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0076","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(0)=∅，Fin(0)=∅。每輸入恰一資料列；待核原序候選rows=[]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([0, 0], [], [], [], [], 是, [])","explanation_zh":"一列協議候選表完整稽核=([0, 0], [], [], [], [], 是, [])。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153076,"parameters":{"n":0,"m":0,"rows":[],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0077","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(1)=[0]，Fin(1)=[0]。每輸入恰一資料列；待核原序候選rows=[[0, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([1, 1], [是], [1], [], [], 是, [0])","explanation_zh":"一列協議候選表完整稽核=([1, 1], [是], [1], [], [], 是, [0])。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153077,"parameters":{"n":1,"m":1,"rows":[[0,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[1,1,[true],[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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0078","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(1)=[0]，Fin(1)=[0]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [0, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([1, 1], [是, 是], [2], [], [0], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([1, 1], [是, 是], [2], [], [0], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153078,"parameters":{"n":1,"m":1,"rows":[[0,0],[0,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[1,1,[true,true],[2],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0079","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(2)=[0, 1]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([2, 2], [是], [1, 0], [1], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([2, 2], [是], [1, 0], [1], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153079,"parameters":{"n":2,"m":2,"rows":[[0,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[2,2,[true],[1,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0080","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(2)=[0, 1]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [1, 2]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([2, 2], [是, 否], [1, 1], [], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([2, 2], [是, 否], [1, 1], [], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153080,"parameters":{"n":2,"m":2,"rows":[[0,0],[1,2]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[2,2,[true,false],[1,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0081","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(2)=[0, 1]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[-1, 0], [0, 0], [1, 1]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([2, 2], [否, 是, 是], [1, 1], [], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([2, 2], [否, 是, 是], [1, 1], [], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153081,"parameters":{"n":2,"m":2,"rows":[[-1,0],[0,0],[1,1]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[2,2,[false,true,true],[1,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0082","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [], [0, 0, 0], [0, 1, 2], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [], [0, 0, 0], [0, 1, 2], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153082,"parameters":{"n":3,"m":2,"rows":[],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[],[0,0,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0083","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是], [1, 0, 0], [1, 2], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是], [1, 0, 0], [1, 2], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":1,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153083,"parameters":{"n":3,"m":2,"rows":[[0,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true],[1,0,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0084","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [0, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是], [2, 0, 0], [1, 2], [0], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是], [2, 0, 0], [1, 2], [0], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153084,"parameters":{"n":3,"m":2,"rows":[[0,0],[0,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[2,0,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0085","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[1, 1]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是], [0, 1, 0], [0, 2], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是], [0, 1, 0], [0, 2], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153085,"parameters":{"n":3,"m":2,"rows":[[1,1]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true],[0,1,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0086","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [1, 1]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是], [1, 1, 0], [2], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是], [1, 1, 0], [2], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153086,"parameters":{"n":3,"m":2,"rows":[[0,0],[1,1]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[1,1,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0087","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [0, 0], [1, 1]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是, 是], [2, 1, 0], [2], [0], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是, 是], [2, 1, 0], [2], [0], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153087,"parameters":{"n":3,"m":2,"rows":[[0,0],[0,0],[1,1]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[2,1,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0088","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[1, 1], [1, 1]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是], [0, 2, 0], [0, 2], [1], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是], [0, 2, 0], [0, 2], [1], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153088,"parameters":{"n":3,"m":2,"rows":[[1,1],[1,1]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[0,2,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0089","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [1, 1], [1, 1]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是, 是], [1, 2, 0], [2], [1], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是, 是], [1, 2, 0], [2], [1], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153089,"parameters":{"n":3,"m":2,"rows":[[0,0],[1,1],[1,1]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[1,2,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0090","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [0, 0], [1, 1], [1, 1]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是, 是, 是], [2, 2, 0], [2], [0, 1], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是, 是, 是], [2, 2, 0], [2], [0, 1], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153090,"parameters":{"n":3,"m":2,"rows":[[0,0],[0,0],[1,1],[1,1]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true,true],[2,2,0],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0091","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是], [0, 0, 1], [0, 1], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是], [0, 0, 1], [0, 1], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153091,"parameters":{"n":3,"m":2,"rows":[[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true],[0,0,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0092","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是], [1, 0, 1], [1], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是], [1, 0, 1], [1], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":2,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153092,"parameters":{"n":3,"m":2,"rows":[[0,0],[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[1,0,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0093","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [0, 0], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是, 是], [2, 0, 1], [1], [0], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是, 是], [2, 0, 1], [1], [0], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153093,"parameters":{"n":3,"m":2,"rows":[[0,0],[0,0],[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[2,0,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0094","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[1, 1], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是], [0, 1, 1], [0], [], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是], [0, 1, 1], [0], [], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153094,"parameters":{"n":3,"m":2,"rows":[[1,1],[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[0,1,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0095","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [1, 1], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是, 是], [1, 1, 1], [], [], 是, [0, 1, 0])","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是, 是], [1, 1, 1], [], [], 是, [0, 1, 0])。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153095,"parameters":{"n":3,"m":2,"rows":[[0,0],[1,1],[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[1,1,1],[0,1,0]]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0096","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [0, 0], [1, 1], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是, 是, 是], [2, 1, 1], [], [0], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是, 是, 是], [2, 1, 1], [], [0], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153096,"parameters":{"n":3,"m":2,"rows":[[0,0],[0,0],[1,1],[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true,true],[2,1,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0097","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[1, 1], [1, 1], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是, 是], [0, 2, 1], [0], [1], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是, 是], [0, 2, 1], [0], [1], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153097,"parameters":{"n":3,"m":2,"rows":[[1,1],[1,1],[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true],[0,2,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0098","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [1, 1], [1, 1], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是, 是, 是], [1, 2, 1], [], [1], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是, 是, 是], [1, 2, 1], [], [1], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153098,"parameters":{"n":3,"m":2,"rows":[[0,0],[1,1],[1,1],[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true,true],[1,2,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0099","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[0, 0], [0, 0], [1, 1], [1, 1], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是, 是, 是, 是], [2, 2, 1], [], [0, 1], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是, 是, 是, 是], [2, 2, 1], [], [0, 1], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153099,"parameters":{"n":3,"m":2,"rows":[[0,0],[0,0],[1,1],[1,1],[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true,true,true,true],[2,2,1],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261011-advance-20261015-r03-domain-codomain-range-0100","batch_id":"batch-20261011-advance-20261015-r03-domain-codomain-range-foundations","language":"zh-Hant","source_mko_ids":["mko-domain-codomain-range"],"title_zh":"一列資料協議完整稽核","stem_zh":"Fin型別從0起，Fin(3)=[0, 1, 2]，Fin(2)=[0, 1]。每輸入恰一資料列；待核原序候選rows=[[2, 0], [2, 0]]。求 ([n,m], 每列雙端型別資格, 每合法輸入的raw出現次數, 漏列輸入, 重複輸入, 完整資格, 合格orderedImages或未成總表)。出現次數先按input計，不因output域外而刪列。","answer":{"kind":"expression","value":"([3, 2], [是, 是], [0, 0, 2], [0, 1], [2], 否, 未成總表)","explanation_zh":"一列協議候選表完整稽核=([3, 2], [是, 是], [0, 0, 2], [0, 1], [2], 否, 未成總表)。所有raw列型別與每個輸入次數分別核對；兩者都合格才形成完整表。同值重複列不符合一列協議不代表多值函數。完整總表非部分程式函數，有限表非一般無限集合證明。"},"difficulty":{"band":"upper_secondary","level":3,"skills":["一列資料協議完整稽核"]},"variant":{"family_id":"qf-density15-typed-mapping-table-candidate-audit","seed":202610153100,"parameters":{"n":3,"m":2,"rows":[[2,0],[2,0]],"domain":"finite_typed_function_data","operation":"density15_typed_mapping_table_candidate_audit","semantic_template":"qf-density15-typed-mapping-table-candidate-audit/[3,2,[true,true],[0,0,2],\"not_total\"]"}},"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":"2026-10-11","contract_version":"ocme-question-factory-v0.1"}}