{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0001","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(0)=∅，images=[]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([], [], [], 是)","explanation_zh":"有限結構核對=([], [], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167001,"parameters":{"n":0,"m":0,"images":[],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[],\"m\":0,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0002","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(2)=[0, 1]，images=[]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([], [[], []], [0, 1], 否)","explanation_zh":"有限結構核對=([], [[], []], [0, 1], 否)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167002,"parameters":{"n":0,"m":2,"images":[],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[],\"m\":2,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0003","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(3)=[0, 1, 2]→Fin(2)=[0, 1]，images=[0, 1, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([0, 1, 1], [[0], [1, 2]], [], 是)","explanation_zh":"有限結構核對=([0, 1, 1], [[0], [1, 2]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167003,"parameters":{"n":3,"m":2,"images":[0,1,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[0,1,1],\"m\":2,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0004","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 0, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [[0, 1, 2, 3], [4], []], [2], 否)","explanation_zh":"有限結構核對=([0, 0, 0, 0, 1], [[0, 1, 2, 3], [4], []], [2], 否)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167004,"parameters":{"n":5,"m":3,"images":[0,0,0,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[0,0,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0005","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 0, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [[1, 2, 3], [0, 4], []], [2], 否)","explanation_zh":"有限結構核對=([1, 0, 0, 0, 1], [[1, 2, 3], [0, 4], []], [2], 否)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167005,"parameters":{"n":5,"m":3,"images":[1,0,0,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[1,0,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0006","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 0, 0, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([2, 0, 0, 0, 1], [[1, 2, 3], [4], [0]], [], 是)","explanation_zh":"有限結構核對=([2, 0, 0, 0, 1], [[1, 2, 3], [4], [0]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167006,"parameters":{"n":5,"m":3,"images":[2,0,0,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[2,0,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0007","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 0, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [[0, 2, 3], [1, 4], []], [2], 否)","explanation_zh":"有限結構核對=([0, 1, 0, 0, 1], [[0, 2, 3], [1, 4], []], [2], 否)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167007,"parameters":{"n":5,"m":3,"images":[0,1,0,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[0,1,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0008","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 0, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [[2, 3], [0, 1, 4], []], [2], 否)","explanation_zh":"有限結構核對=([1, 1, 0, 0, 1], [[2, 3], [0, 1, 4], []], [2], 否)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167008,"parameters":{"n":5,"m":3,"images":[1,1,0,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[1,1,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0009","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 1, 0, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([2, 1, 0, 0, 1], [[2, 3], [1, 4], [0]], [], 是)","explanation_zh":"有限結構核對=([2, 1, 0, 0, 1], [[2, 3], [1, 4], [0]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167009,"parameters":{"n":5,"m":3,"images":[2,1,0,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[2,1,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0010","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 2, 0, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([0, 2, 0, 0, 1], [[0, 2, 3], [4], [1]], [], 是)","explanation_zh":"有限結構核對=([0, 2, 0, 0, 1], [[0, 2, 3], [4], [1]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167010,"parameters":{"n":5,"m":3,"images":[0,2,0,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[0,2,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0011","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 2, 0, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([1, 2, 0, 0, 1], [[2, 3], [0, 4], [1]], [], 是)","explanation_zh":"有限結構核對=([1, 2, 0, 0, 1], [[2, 3], [0, 4], [1]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167011,"parameters":{"n":5,"m":3,"images":[1,2,0,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[1,2,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0012","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 2, 0, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([2, 2, 0, 0, 1], [[2, 3], [4], [0, 1]], [], 是)","explanation_zh":"有限結構核對=([2, 2, 0, 0, 1], [[2, 3], [4], [0, 1]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167012,"parameters":{"n":5,"m":3,"images":[2,2,0,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[2,2,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0013","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 1, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [[0, 1, 3], [2, 4], []], [2], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 0, 1], [[0, 1, 3], [2, 4], []], [2], 否)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167013,"parameters":{"n":5,"m":3,"images":[0,0,1,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[0,0,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0014","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 1, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], [[1, 3], [0, 2, 4], []], [2], 否)","explanation_zh":"有限結構核對=([1, 0, 1, 0, 1], [[1, 3], [0, 2, 4], []], [2], 否)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167014,"parameters":{"n":5,"m":3,"images":[1,0,1,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[1,0,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0015","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 0, 1, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([2, 0, 1, 0, 1], [[1, 3], [2, 4], [0]], [], 是)","explanation_zh":"有限結構核對=([2, 0, 1, 0, 1], [[1, 3], [2, 4], [0]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167015,"parameters":{"n":5,"m":3,"images":[2,0,1,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[2,0,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0016","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 1, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 1], [[0, 3], [1, 2, 4], []], [2], 否)","explanation_zh":"有限結構核對=([0, 1, 1, 0, 1], [[0, 3], [1, 2, 4], []], [2], 否)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167016,"parameters":{"n":5,"m":3,"images":[0,1,1,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[0,1,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0017","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 1, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 1], [[3], [0, 1, 2, 4], []], [2], 否)","explanation_zh":"有限結構核對=([1, 1, 1, 0, 1], [[3], [0, 1, 2, 4], []], [2], 否)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167017,"parameters":{"n":5,"m":3,"images":[1,1,1,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[1,1,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0018","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 1, 1, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([2, 1, 1, 0, 1], [[3], [1, 2, 4], [0]], [], 是)","explanation_zh":"有限結構核對=([2, 1, 1, 0, 1], [[3], [1, 2, 4], [0]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167018,"parameters":{"n":5,"m":3,"images":[2,1,1,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[2,1,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0019","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 2, 1, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([0, 2, 1, 0, 1], [[0, 3], [2, 4], [1]], [], 是)","explanation_zh":"有限結構核對=([0, 2, 1, 0, 1], [[0, 3], [2, 4], [1]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167019,"parameters":{"n":5,"m":3,"images":[0,2,1,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[0,2,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0020","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 2, 1, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([1, 2, 1, 0, 1], [[3], [0, 2, 4], [1]], [], 是)","explanation_zh":"有限結構核對=([1, 2, 1, 0, 1], [[3], [0, 2, 4], [1]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167020,"parameters":{"n":5,"m":3,"images":[1,2,1,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[1,2,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0021","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 2, 1, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([2, 2, 1, 0, 1], [[3], [2, 4], [0, 1]], [], 是)","explanation_zh":"有限結構核對=([2, 2, 1, 0, 1], [[3], [2, 4], [0, 1]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167021,"parameters":{"n":5,"m":3,"images":[2,2,1,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[2,2,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0022","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 2, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([0, 0, 2, 0, 1], [[0, 1, 3], [4], [2]], [], 是)","explanation_zh":"有限結構核對=([0, 0, 2, 0, 1], [[0, 1, 3], [4], [2]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167022,"parameters":{"n":5,"m":3,"images":[0,0,2,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[0,0,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0023","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 2, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([1, 0, 2, 0, 1], [[1, 3], [0, 4], [2]], [], 是)","explanation_zh":"有限結構核對=([1, 0, 2, 0, 1], [[1, 3], [0, 4], [2]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167023,"parameters":{"n":5,"m":3,"images":[1,0,2,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[1,0,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0024","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 0, 2, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([2, 0, 2, 0, 1], [[1, 3], [4], [0, 2]], [], 是)","explanation_zh":"有限結構核對=([2, 0, 2, 0, 1], [[1, 3], [4], [0, 2]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167024,"parameters":{"n":5,"m":3,"images":[2,0,2,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[2,0,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0025","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"陪域全纖維與缺目標","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 2, 0, 1]。求 (原images, 按陪域0到m−1的全部纖維, 缺目標, 滿射資格)。空陪域的纖維列為空。","answer":{"kind":"expression","value":"([0, 1, 2, 0, 1], [[0, 3], [1, 4], [2]], [], 是)","explanation_zh":"有限結構核對=([0, 1, 2, 0, 1], [[0, 3], [1, 4], [2]], [], 是)。每個宣告目標都列來源索引；只要有一個空纖維即不滿射。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["陪域全纖維與缺目標"]},"variant":{"family_id":"qf-density16-surj-fiber-inventory","seed":202610167025,"parameters":{"n":5,"m":3,"images":[0,1,2,0,1],"domain":"Fin_total_table","operation":"surj-fiber-inventory","semantic_template":"qf-density16-surj-fiber-inventory/{\"images\":[0,1,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0026","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(0)=∅，images=[]。候選新陪域原序codomain=[]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([], [], 是, [], 是)","explanation_zh":"有限結構核對=([], [], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167026,"parameters":{"n":0,"m":0,"images":[],"codomain":[],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[],\"images\":[],\"m\":0,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0027","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(1)=[0]，images=[]。候選新陪域原序codomain=[-1]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([], [-1], 是, [-1], 否)","explanation_zh":"有限結構核對=([], [-1], 是, [-1], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167027,"parameters":{"n":0,"m":1,"images":[],"codomain":[-1],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[-1],\"images\":[],\"m\":1,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0028","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(2)=[0, 1]→Fin(3)=[0, 1, 2]，images=[0, 1]。候選新陪域原序codomain=[0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 1], [0], 否, 不合陪域, 不求值)","explanation_zh":"有限結構核對=([0, 1], [0], 否, 不合陪域, 不求值)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167028,"parameters":{"n":2,"m":3,"images":[0,1],"codomain":[0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0],\"images\":[0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0029","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(2)=[0, 1]→Fin(3)=[0, 1, 2]，images=[0, 1]。候選新陪域原序codomain=[1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 1], [0, 1], 是, [], 是)","explanation_zh":"有限結構核對=([0, 1], [0, 1], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167029,"parameters":{"n":2,"m":3,"images":[0,1],"codomain":[1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1],\"images\":[0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0030","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(2)=[0, 1]→Fin(3)=[0, 1, 2]，images=[0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 1], [0, 1, 2], 是, [2], 否)","explanation_zh":"有限結構核對=([0, 1], [0, 1, 2], 是, [2], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167030,"parameters":{"n":2,"m":3,"images":[0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0031","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 0, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [0, 1, 2], 是, [2], 否)","explanation_zh":"有限結構核對=([0, 0, 0, 0, 1], [0, 1, 2], 是, [2], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167031,"parameters":{"n":5,"m":3,"images":[0,0,0,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[0,0,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0032","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 0, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [0, 1, 2], 是, [2], 否)","explanation_zh":"有限結構核對=([1, 0, 0, 0, 1], [0, 1, 2], 是, [2], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167032,"parameters":{"n":5,"m":3,"images":[1,0,0,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[1,0,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0033","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 0, 0, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([2, 0, 0, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([2, 0, 0, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167033,"parameters":{"n":5,"m":3,"images":[2,0,0,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[2,0,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0034","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 0, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [0, 1, 2], 是, [2], 否)","explanation_zh":"有限結構核對=([0, 1, 0, 0, 1], [0, 1, 2], 是, [2], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167034,"parameters":{"n":5,"m":3,"images":[0,1,0,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[0,1,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0035","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 0, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [0, 1, 2], 是, [2], 否)","explanation_zh":"有限結構核對=([1, 1, 0, 0, 1], [0, 1, 2], 是, [2], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167035,"parameters":{"n":5,"m":3,"images":[1,1,0,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[1,1,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0036","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 1, 0, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([2, 1, 0, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([2, 1, 0, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167036,"parameters":{"n":5,"m":3,"images":[2,1,0,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[2,1,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0037","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 2, 0, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 2, 0, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([0, 2, 0, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167037,"parameters":{"n":5,"m":3,"images":[0,2,0,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[0,2,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0038","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 2, 0, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([1, 2, 0, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([1, 2, 0, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167038,"parameters":{"n":5,"m":3,"images":[1,2,0,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[1,2,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0039","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 2, 0, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([2, 2, 0, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([2, 2, 0, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167039,"parameters":{"n":5,"m":3,"images":[2,2,0,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[2,2,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0040","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 1, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [0, 1, 2], 是, [2], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 0, 1], [0, 1, 2], 是, [2], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167040,"parameters":{"n":5,"m":3,"images":[0,0,1,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[0,0,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0041","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 1, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], [0, 1, 2], 是, [2], 否)","explanation_zh":"有限結構核對=([1, 0, 1, 0, 1], [0, 1, 2], 是, [2], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167041,"parameters":{"n":5,"m":3,"images":[1,0,1,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[1,0,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0042","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 0, 1, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([2, 0, 1, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([2, 0, 1, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167042,"parameters":{"n":5,"m":3,"images":[2,0,1,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[2,0,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0043","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 1, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 1], [0, 1, 2], 是, [2], 否)","explanation_zh":"有限結構核對=([0, 1, 1, 0, 1], [0, 1, 2], 是, [2], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167043,"parameters":{"n":5,"m":3,"images":[0,1,1,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[0,1,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0044","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 1, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 1], [0, 1, 2], 是, [2], 否)","explanation_zh":"有限結構核對=([1, 1, 1, 0, 1], [0, 1, 2], 是, [2], 否)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167044,"parameters":{"n":5,"m":3,"images":[1,1,1,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[1,1,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0045","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 1, 1, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([2, 1, 1, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([2, 1, 1, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167045,"parameters":{"n":5,"m":3,"images":[2,1,1,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[2,1,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0046","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 2, 1, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 2, 1, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([0, 2, 1, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167046,"parameters":{"n":5,"m":3,"images":[0,2,1,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[0,2,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0047","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 2, 1, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([1, 2, 1, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([1, 2, 1, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167047,"parameters":{"n":5,"m":3,"images":[1,2,1,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[1,2,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0048","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 2, 1, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([2, 2, 1, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([2, 2, 1, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167048,"parameters":{"n":5,"m":3,"images":[2,2,1,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[2,2,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0049","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 2, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([0, 0, 2, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([0, 0, 2, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167049,"parameters":{"n":5,"m":3,"images":[0,0,2,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[0,0,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0050","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"新陪域的全表資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 2, 0, 1]。候選新陪域原序codomain=[2, 1, 0]，可用原Fin(m)外的相異整數標籤。求 (原images, 排序新陪域, 全原輸出合新陪域資格, 合格時缺目標或不合陪域, 滿射資格或不求值)。","answer":{"kind":"expression","value":"([1, 0, 2, 0, 1], [0, 1, 2], 是, [], 是)","explanation_zh":"有限結構核對=([1, 0, 2, 0, 1], [0, 1, 2], 是, [], 是)。先核每個仍存在的原輸出；全部落在新陪域才列新缺目標，不丟掉輸出來洗白。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["新陪域的全表資格"]},"variant":{"family_id":"qf-density16-surj-changed-codomain-qualification","seed":202610167050,"parameters":{"n":5,"m":3,"images":[1,0,2,0,1],"codomain":[2,1,0],"domain":"Fin_total_table","operation":"surj-changed-codomain-qualification","semantic_template":"qf-density16-surj-changed-codomain-qualification/{\"codomain\":[0,1,2],\"images\":[1,0,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0051","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(1)=[0]→Fin(1)=[0]，images=[0]。刪原輸入at=0，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0], [], [], [], [0], 否)","explanation_zh":"有限結構核對=([0], [], [], [], [0], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167051,"parameters":{"n":1,"m":1,"images":[0],"at":0,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":0,\"images\":[0],\"m\":1,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0052","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(3)=[0, 1, 2]→Fin(2)=[0, 1]，images=[0, 1, 1]。刪原輸入at=1，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 1, 1], [], [0, 2], [0, 1], [], 是)","explanation_zh":"有限結構核對=([0, 1, 1], [], [0, 2], [0, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167052,"parameters":{"n":3,"m":2,"images":[0,1,1],"at":1,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":1,\"images\":[0,1,1],\"m\":2,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0053","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(3)=[0, 1, 2]→Fin(3)=[0, 1, 2]，images=[0, 1, 1]。刪原輸入at=2，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 1, 1], [2], [0, 1], [0, 1], [2], 否)","explanation_zh":"有限結構核對=([0, 1, 1], [2], [0, 1], [0, 1], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167053,"parameters":{"n":3,"m":3,"images":[0,1,1],"at":2,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":2,\"images\":[0,1,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0054","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 0, 0, 1]。刪原輸入at=0，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [2], [1, 2, 3, 4], [0, 0, 0, 1], [2], 否)","explanation_zh":"有限結構核對=([0, 0, 0, 0, 1], [2], [1, 2, 3, 4], [0, 0, 0, 1], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167054,"parameters":{"n":5,"m":3,"images":[0,0,0,0,1],"at":0,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":0,\"images\":[0,0,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0055","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 0, 0, 1]。刪原輸入at=1，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [2], [0, 2, 3, 4], [1, 0, 0, 1], [2], 否)","explanation_zh":"有限結構核對=([1, 0, 0, 0, 1], [2], [0, 2, 3, 4], [1, 0, 0, 1], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167055,"parameters":{"n":5,"m":3,"images":[1,0,0,0,1],"at":1,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":1,\"images\":[1,0,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0056","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 0, 0, 0, 1]。刪原輸入at=2，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([2, 0, 0, 0, 1], [], [0, 1, 3, 4], [2, 0, 0, 1], [], 是)","explanation_zh":"有限結構核對=([2, 0, 0, 0, 1], [], [0, 1, 3, 4], [2, 0, 0, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167056,"parameters":{"n":5,"m":3,"images":[2,0,0,0,1],"at":2,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":2,\"images\":[2,0,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0057","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 0, 0, 1]。刪原輸入at=3，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [2], [0, 1, 2, 4], [0, 1, 0, 1], [2], 否)","explanation_zh":"有限結構核對=([0, 1, 0, 0, 1], [2], [0, 1, 2, 4], [0, 1, 0, 1], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167057,"parameters":{"n":5,"m":3,"images":[0,1,0,0,1],"at":3,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":3,\"images\":[0,1,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0058","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 0, 0, 1]。刪原輸入at=4，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [2], [0, 1, 2, 3], [1, 1, 0, 0], [2], 否)","explanation_zh":"有限結構核對=([1, 1, 0, 0, 1], [2], [0, 1, 2, 3], [1, 1, 0, 0], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167058,"parameters":{"n":5,"m":3,"images":[1,1,0,0,1],"at":4,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":4,\"images\":[1,1,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0059","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 1, 0, 0, 1]。刪原輸入at=0，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([2, 1, 0, 0, 1], [], [1, 2, 3, 4], [1, 0, 0, 1], [2], 否)","explanation_zh":"有限結構核對=([2, 1, 0, 0, 1], [], [1, 2, 3, 4], [1, 0, 0, 1], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167059,"parameters":{"n":5,"m":3,"images":[2,1,0,0,1],"at":0,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":0,\"images\":[2,1,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0060","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 2, 0, 0, 1]。刪原輸入at=1，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 2, 0, 0, 1], [], [0, 2, 3, 4], [0, 0, 0, 1], [2], 否)","explanation_zh":"有限結構核對=([0, 2, 0, 0, 1], [], [0, 2, 3, 4], [0, 0, 0, 1], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167060,"parameters":{"n":5,"m":3,"images":[0,2,0,0,1],"at":1,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":1,\"images\":[0,2,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0061","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 2, 0, 0, 1]。刪原輸入at=2，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([1, 2, 0, 0, 1], [], [0, 1, 3, 4], [1, 2, 0, 1], [], 是)","explanation_zh":"有限結構核對=([1, 2, 0, 0, 1], [], [0, 1, 3, 4], [1, 2, 0, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167061,"parameters":{"n":5,"m":3,"images":[1,2,0,0,1],"at":2,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":2,\"images\":[1,2,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0062","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 2, 0, 0, 1]。刪原輸入at=3，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([2, 2, 0, 0, 1], [], [0, 1, 2, 4], [2, 2, 0, 1], [], 是)","explanation_zh":"有限結構核對=([2, 2, 0, 0, 1], [], [0, 1, 2, 4], [2, 2, 0, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167062,"parameters":{"n":5,"m":3,"images":[2,2,0,0,1],"at":3,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":3,\"images\":[2,2,0,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0063","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 1, 0, 1]。刪原輸入at=4，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [2], [0, 1, 2, 3], [0, 0, 1, 0], [2], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 0, 1], [2], [0, 1, 2, 3], [0, 0, 1, 0], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167063,"parameters":{"n":5,"m":3,"images":[0,0,1,0,1],"at":4,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":4,\"images\":[0,0,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0064","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 1, 0, 1]。刪原輸入at=0，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], [2], [1, 2, 3, 4], [0, 1, 0, 1], [2], 否)","explanation_zh":"有限結構核對=([1, 0, 1, 0, 1], [2], [1, 2, 3, 4], [0, 1, 0, 1], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167064,"parameters":{"n":5,"m":3,"images":[1,0,1,0,1],"at":0,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":0,\"images\":[1,0,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0065","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 0, 1, 0, 1]。刪原輸入at=1，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([2, 0, 1, 0, 1], [], [0, 2, 3, 4], [2, 1, 0, 1], [], 是)","explanation_zh":"有限結構核對=([2, 0, 1, 0, 1], [], [0, 2, 3, 4], [2, 1, 0, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167065,"parameters":{"n":5,"m":3,"images":[2,0,1,0,1],"at":1,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":1,\"images\":[2,0,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0066","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 1, 0, 1]。刪原輸入at=2，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 1], [2], [0, 1, 3, 4], [0, 1, 0, 1], [2], 否)","explanation_zh":"有限結構核對=([0, 1, 1, 0, 1], [2], [0, 1, 3, 4], [0, 1, 0, 1], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167066,"parameters":{"n":5,"m":3,"images":[0,1,1,0,1],"at":2,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":2,\"images\":[0,1,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0067","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 1, 0, 1]。刪原輸入at=3，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 1], [2], [0, 1, 2, 4], [1, 1, 1, 1], [0, 2], 否)","explanation_zh":"有限結構核對=([1, 1, 1, 0, 1], [2], [0, 1, 2, 4], [1, 1, 1, 1], [0, 2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167067,"parameters":{"n":5,"m":3,"images":[1,1,1,0,1],"at":3,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":3,\"images\":[1,1,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0068","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 1, 1, 0, 1]。刪原輸入at=4，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([2, 1, 1, 0, 1], [], [0, 1, 2, 3], [2, 1, 1, 0], [], 是)","explanation_zh":"有限結構核對=([2, 1, 1, 0, 1], [], [0, 1, 2, 3], [2, 1, 1, 0], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167068,"parameters":{"n":5,"m":3,"images":[2,1,1,0,1],"at":4,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":4,\"images\":[2,1,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0069","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 2, 1, 0, 1]。刪原輸入at=0，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 2, 1, 0, 1], [], [1, 2, 3, 4], [2, 1, 0, 1], [], 是)","explanation_zh":"有限結構核對=([0, 2, 1, 0, 1], [], [1, 2, 3, 4], [2, 1, 0, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167069,"parameters":{"n":5,"m":3,"images":[0,2,1,0,1],"at":0,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":0,\"images\":[0,2,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0070","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 2, 1, 0, 1]。刪原輸入at=1，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([1, 2, 1, 0, 1], [], [0, 2, 3, 4], [1, 1, 0, 1], [2], 否)","explanation_zh":"有限結構核對=([1, 2, 1, 0, 1], [], [0, 2, 3, 4], [1, 1, 0, 1], [2], 否)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167070,"parameters":{"n":5,"m":3,"images":[1,2,1,0,1],"at":1,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":1,\"images\":[1,2,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0071","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 2, 1, 0, 1]。刪原輸入at=2，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([2, 2, 1, 0, 1], [], [0, 1, 3, 4], [2, 2, 0, 1], [], 是)","explanation_zh":"有限結構核對=([2, 2, 1, 0, 1], [], [0, 1, 3, 4], [2, 2, 0, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167071,"parameters":{"n":5,"m":3,"images":[2,2,1,0,1],"at":2,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":2,\"images\":[2,2,1,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0072","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 2, 0, 1]。刪原輸入at=3，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 0, 2, 0, 1], [], [0, 1, 2, 4], [0, 0, 2, 1], [], 是)","explanation_zh":"有限結構核對=([0, 0, 2, 0, 1], [], [0, 1, 2, 4], [0, 0, 2, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167072,"parameters":{"n":5,"m":3,"images":[0,0,2,0,1],"at":3,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":3,\"images\":[0,0,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0073","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 2, 0, 1]。刪原輸入at=4，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([1, 0, 2, 0, 1], [], [0, 1, 2, 3], [1, 0, 2, 0], [], 是)","explanation_zh":"有限結構核對=([1, 0, 2, 0, 1], [], [0, 1, 2, 3], [1, 0, 2, 0], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167073,"parameters":{"n":5,"m":3,"images":[1,0,2,0,1],"at":4,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":4,\"images\":[1,0,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0074","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[2, 0, 2, 0, 1]。刪原輸入at=0，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([2, 0, 2, 0, 1], [], [1, 2, 3, 4], [0, 2, 0, 1], [], 是)","explanation_zh":"有限結構核對=([2, 0, 2, 0, 1], [], [1, 2, 3, 4], [0, 2, 0, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167074,"parameters":{"n":5,"m":3,"images":[2,0,2,0,1],"at":0,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":0,\"images\":[2,0,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0075","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"刪一輸入的缺目標變化","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 2, 0, 1]。刪原輸入at=1，原陪域保留。求 (原images, 原缺目標, 保留原輸入標籤, 剩餘images, 後缺目標, 後滿射資格)。","answer":{"kind":"expression","value":"([0, 1, 2, 0, 1], [], [0, 2, 3, 4], [0, 2, 0, 1], [], 是)","explanation_zh":"有限結構核對=([0, 1, 2, 0, 1], [], [0, 2, 3, 4], [0, 2, 0, 1], [], 是)。保留原陪域，刪除該來源後重新收集輸出；移去唯一原像會新增缺目標。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["刪一輸入的缺目標變化"]},"variant":{"family_id":"qf-density16-surj-delete-input-missing","seed":202610167075,"parameters":{"n":5,"m":3,"images":[0,1,2,0,1],"at":1,"domain":"Fin_total_table","operation":"surj-delete-input-missing","semantic_template":"qf-density16-surj-delete-input-missing/{\"at\":1,\"images\":[0,1,2,0,1],\"m\":3,\"n\":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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0076","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(0)=∅，images=[]。有序候選目標queries=[0, -1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([], [否, 否], [不合陪域, 不合陪域], [不合陪域, 不合陪域])","explanation_zh":"有限結構核對=([], [否, 否], [不合陪域, 不合陪域], [不合陪域, 不合陪域])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167076,"parameters":{"n":0,"m":0,"images":[],"queries":[0,-1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[],\"m\":0,\"n\":0,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0077","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(2)=[0, 1]，images=[]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([], [是, 是], [[], []], [不存在, 不存在])","explanation_zh":"有限結構核對=([], [是, 是], [[], []], [不存在, 不存在])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167077,"parameters":{"n":0,"m":2,"images":[],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[],\"m\":2,\"n\":0,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0078","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(3)=[0, 1, 2]→Fin(3)=[0, 1, 2]，images=[0, 0, 1]。有序候選目標queries=[2, 3]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 0, 1], [是, 否], [[], 不合陪域], [不存在, 不合陪域])","explanation_zh":"有限結構核對=([0, 0, 1], [是, 否], [[], 不合陪域], [不存在, 不合陪域])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167078,"parameters":{"n":3,"m":3,"images":[0,0,1],"queries":[2,3],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,0,1],\"m\":3,\"n\":3,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0079","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(3)=[0, 1, 2]→Fin(2)=[0, 1]，images=[0, 0, 1]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 0, 1], [是, 是], [[0, 1], [2]], [0, 2])","explanation_zh":"有限結構核對=([0, 0, 1], [是, 是], [[0, 1], [2]], [0, 2])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167079,"parameters":{"n":3,"m":2,"images":[0,0,1],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,0,1],\"m\":2,\"n\":3,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0080","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 0, 0, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 0], [是, 是], [[0, 1, 2, 3, 4], []], [0, 不存在])","explanation_zh":"有限結構核對=([0, 0, 0, 0, 0], [是, 是], [[0, 1, 2, 3, 4], []], [0, 不存在])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167080,"parameters":{"n":5,"m":3,"images":[0,0,0,0,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,0,0,0,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0081","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 0, 0, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 0], [是, 是], [[1, 2, 3, 4], [0]], [1, 0])","explanation_zh":"有限結構核對=([1, 0, 0, 0, 0], [是, 是], [[1, 2, 3, 4], [0]], [1, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167081,"parameters":{"n":5,"m":3,"images":[1,0,0,0,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,0,0,0,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0082","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 0, 0, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 0], [是, 是], [[0, 2, 3, 4], [1]], [0, 1])","explanation_zh":"有限結構核對=([0, 1, 0, 0, 0], [是, 是], [[0, 2, 3, 4], [1]], [0, 1])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167082,"parameters":{"n":5,"m":3,"images":[0,1,0,0,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,1,0,0,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0083","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 0, 0, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 0], [是, 是], [[2, 3, 4], [0, 1]], [2, 0])","explanation_zh":"有限結構核對=([1, 1, 0, 0, 0], [是, 是], [[2, 3, 4], [0, 1]], [2, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167083,"parameters":{"n":5,"m":3,"images":[1,1,0,0,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,1,0,0,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0084","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 1, 0, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 0], [是, 是], [[0, 1, 3, 4], [2]], [0, 2])","explanation_zh":"有限結構核對=([0, 0, 1, 0, 0], [是, 是], [[0, 1, 3, 4], [2]], [0, 2])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167084,"parameters":{"n":5,"m":3,"images":[0,0,1,0,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,0,1,0,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0085","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 1, 0, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 0], [是, 是], [[1, 3, 4], [0, 2]], [1, 0])","explanation_zh":"有限結構核對=([1, 0, 1, 0, 0], [是, 是], [[1, 3, 4], [0, 2]], [1, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167085,"parameters":{"n":5,"m":3,"images":[1,0,1,0,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,0,1,0,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0086","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 1, 0, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 0], [是, 是], [[0, 3, 4], [1, 2]], [0, 1])","explanation_zh":"有限結構核對=([0, 1, 1, 0, 0], [是, 是], [[0, 3, 4], [1, 2]], [0, 1])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167086,"parameters":{"n":5,"m":3,"images":[0,1,1,0,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,1,1,0,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0087","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 1, 0, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 0], [是, 是], [[3, 4], [0, 1, 2]], [3, 0])","explanation_zh":"有限結構核對=([1, 1, 1, 0, 0], [是, 是], [[3, 4], [0, 1, 2]], [3, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167087,"parameters":{"n":5,"m":3,"images":[1,1,1,0,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,1,1,0,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0088","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 0, 1, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 0, 0, 1, 0], [是, 是], [[0, 1, 2, 4], [3]], [0, 3])","explanation_zh":"有限結構核對=([0, 0, 0, 1, 0], [是, 是], [[0, 1, 2, 4], [3]], [0, 3])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167088,"parameters":{"n":5,"m":3,"images":[0,0,0,1,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,0,0,1,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0089","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 0, 1, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 0, 0, 1, 0], [是, 是], [[1, 2, 4], [0, 3]], [1, 0])","explanation_zh":"有限結構核對=([1, 0, 0, 1, 0], [是, 是], [[1, 2, 4], [0, 3]], [1, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167089,"parameters":{"n":5,"m":3,"images":[1,0,0,1,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,0,0,1,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0090","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 0, 1, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 1, 0, 1, 0], [是, 是], [[0, 2, 4], [1, 3]], [0, 1])","explanation_zh":"有限結構核對=([0, 1, 0, 1, 0], [是, 是], [[0, 2, 4], [1, 3]], [0, 1])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167090,"parameters":{"n":5,"m":3,"images":[0,1,0,1,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,1,0,1,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0091","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 0, 1, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 1, 0, 1, 0], [是, 是], [[2, 4], [0, 1, 3]], [2, 0])","explanation_zh":"有限結構核對=([1, 1, 0, 1, 0], [是, 是], [[2, 4], [0, 1, 3]], [2, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167091,"parameters":{"n":5,"m":3,"images":[1,1,0,1,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,1,0,1,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0092","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 1, 1, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 0, 1, 1, 0], [是, 是], [[0, 1, 4], [2, 3]], [0, 2])","explanation_zh":"有限結構核對=([0, 0, 1, 1, 0], [是, 是], [[0, 1, 4], [2, 3]], [0, 2])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167092,"parameters":{"n":5,"m":3,"images":[0,0,1,1,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,0,1,1,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0093","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 1, 1, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 0, 1, 1, 0], [是, 是], [[1, 4], [0, 2, 3]], [1, 0])","explanation_zh":"有限結構核對=([1, 0, 1, 1, 0], [是, 是], [[1, 4], [0, 2, 3]], [1, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167093,"parameters":{"n":5,"m":3,"images":[1,0,1,1,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,0,1,1,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0094","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 1, 1, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 1, 1, 1, 0], [是, 是], [[0, 4], [1, 2, 3]], [0, 1])","explanation_zh":"有限結構核對=([0, 1, 1, 1, 0], [是, 是], [[0, 4], [1, 2, 3]], [0, 1])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167094,"parameters":{"n":5,"m":3,"images":[0,1,1,1,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,1,1,1,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0095","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 1, 1, 0]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 1, 1, 1, 0], [是, 是], [[4], [0, 1, 2, 3]], [4, 0])","explanation_zh":"有限結構核對=([1, 1, 1, 1, 0], [是, 是], [[4], [0, 1, 2, 3]], [4, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167095,"parameters":{"n":5,"m":3,"images":[1,1,1,1,0],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,1,1,1,0],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0096","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 0, 0, 1]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [是, 是], [[0, 1, 2, 3], [4]], [0, 4])","explanation_zh":"有限結構核對=([0, 0, 0, 0, 1], [是, 是], [[0, 1, 2, 3], [4]], [0, 4])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167096,"parameters":{"n":5,"m":3,"images":[0,0,0,0,1],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,0,0,0,1],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0097","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 0, 0, 0, 1]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [是, 是], [[1, 2, 3], [0, 4]], [1, 0])","explanation_zh":"有限結構核對=([1, 0, 0, 0, 1], [是, 是], [[1, 2, 3], [0, 4]], [1, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167097,"parameters":{"n":5,"m":3,"images":[1,0,0,0,1],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,0,0,0,1],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0098","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 1, 0, 0, 1]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [是, 是], [[0, 2, 3], [1, 4]], [0, 1])","explanation_zh":"有限結構核對=([0, 1, 0, 0, 1], [是, 是], [[0, 2, 3], [1, 4]], [0, 1])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167098,"parameters":{"n":5,"m":3,"images":[0,1,0,0,1],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,1,0,0,1],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0099","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[1, 1, 0, 0, 1]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [是, 是], [[2, 3], [0, 1, 4]], [2, 0])","explanation_zh":"有限結構核對=([1, 1, 0, 0, 1], [是, 是], [[2, 3], [0, 1, 4]], [2, 0])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167099,"parameters":{"n":5,"m":3,"images":[1,1,0,0,1],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[1,1,0,0,1],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r07-surjective-0100","batch_id":"batch-20261012-advance-20261016-r07-surjective-foundations","language":"zh-Hant","source_mko_ids":["mko-surjective"],"title_zh":"兩個目標的原像與資格","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(3)=[0, 1, 2]，images=[0, 0, 1, 0, 1]。有序候選目標queries=[0, 1]。求 (原images, 兩個陪域資格, 兩個纖維或不合陪域, 各最小原像或不存在/不合陪域)。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [是, 是], [[0, 1, 3], [2, 4]], [0, 2])","explanation_zh":"有限結構核對=([0, 0, 1, 0, 1], [是, 是], [[0, 1, 3], [2, 4]], [0, 2])。合型目標才掃完整表；合法空纖維答不存在，不和域外資格混同。有限精確核對不是一般形式證明。先資格後求值，空函數條件依宣告陪域。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["兩個目標的原像與資格"]},"variant":{"family_id":"qf-density16-surj-two-target-preimages","seed":202610167100,"parameters":{"n":5,"m":3,"images":[0,0,1,0,1],"queries":[0,1],"domain":"Fin_total_table","operation":"surj-two-target-preimages","semantic_template":"qf-density16-surj-two-target-preimages/{\"images\":[0,0,1,0,1],\"m\":3,\"n\":5,\"queries\":[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":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}