{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0001","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(0)=∅，images=[]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([], [], 是)","explanation_zh":"有限結構核對=([], [], 是)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166001,"parameters":{"n":0,"m":0,"images":[],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"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-r06-injective-0002","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(1)=[0]→Fin(1)=[0]，images=[0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0], [], 是)","explanation_zh":"有限結構核對=([0], [], 是)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166002,"parameters":{"n":1,"m":1,"images":[0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"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-r06-injective-0003","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","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, 2]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 1, 2], [], 是)","explanation_zh":"有限結構核對=([0, 1, 2], [], 是)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166003,"parameters":{"n":3,"m":3,"images":[0,1,2],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,1,2],\"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-r06-injective-0004","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 0, 0, 0, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 0], [[0, 1], [0, 2], [0, 3], [0, 4], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]], 否)","explanation_zh":"有限結構核對=([0, 0, 0, 0, 0], [[0, 1], [0, 2], [0, 3], [0, 4], [1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166004,"parameters":{"n":5,"m":2,"images":[0,0,0,0,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,0,0,0,0],\"m\":2,\"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-r06-injective-0005","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 0, 0, 0, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 0], [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]], 否)","explanation_zh":"有限結構核對=([1, 0, 0, 0, 0], [[1, 2], [1, 3], [1, 4], [2, 3], [2, 4], [3, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166005,"parameters":{"n":5,"m":2,"images":[1,0,0,0,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,0,0,0,0],\"m\":2,\"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-r06-injective-0006","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 1, 0, 0, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 0], [[0, 2], [0, 3], [0, 4], [2, 3], [2, 4], [3, 4]], 否)","explanation_zh":"有限結構核對=([0, 1, 0, 0, 0], [[0, 2], [0, 3], [0, 4], [2, 3], [2, 4], [3, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166006,"parameters":{"n":5,"m":2,"images":[0,1,0,0,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,1,0,0,0],\"m\":2,\"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-r06-injective-0007","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 1, 0, 0, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 0], [[0, 1], [2, 3], [2, 4], [3, 4]], 否)","explanation_zh":"有限結構核對=([1, 1, 0, 0, 0], [[0, 1], [2, 3], [2, 4], [3, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166007,"parameters":{"n":5,"m":2,"images":[1,1,0,0,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,1,0,0,0],\"m\":2,\"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-r06-injective-0008","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 0, 1, 0, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 0], [[0, 1], [0, 3], [0, 4], [1, 3], [1, 4], [3, 4]], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 0, 0], [[0, 1], [0, 3], [0, 4], [1, 3], [1, 4], [3, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166008,"parameters":{"n":5,"m":2,"images":[0,0,1,0,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,0,1,0,0],\"m\":2,\"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-r06-injective-0009","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 0, 1, 0, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 0], [[0, 2], [1, 3], [1, 4], [3, 4]], 否)","explanation_zh":"有限結構核對=([1, 0, 1, 0, 0], [[0, 2], [1, 3], [1, 4], [3, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166009,"parameters":{"n":5,"m":2,"images":[1,0,1,0,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,0,1,0,0],\"m\":2,\"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-r06-injective-0010","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 1, 1, 0, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 0], [[0, 3], [0, 4], [1, 2], [3, 4]], 否)","explanation_zh":"有限結構核對=([0, 1, 1, 0, 0], [[0, 3], [0, 4], [1, 2], [3, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166010,"parameters":{"n":5,"m":2,"images":[0,1,1,0,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,1,1,0,0],\"m\":2,\"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-r06-injective-0011","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 1, 1, 0, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 0], [[0, 1], [0, 2], [1, 2], [3, 4]], 否)","explanation_zh":"有限結構核對=([1, 1, 1, 0, 0], [[0, 1], [0, 2], [1, 2], [3, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166011,"parameters":{"n":5,"m":2,"images":[1,1,1,0,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,1,1,0,0],\"m\":2,\"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-r06-injective-0012","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 0, 0, 1, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 0, 0, 1, 0], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], 否)","explanation_zh":"有限結構核對=([0, 0, 0, 1, 0], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166012,"parameters":{"n":5,"m":2,"images":[0,0,0,1,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,0,0,1,0],\"m\":2,\"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-r06-injective-0013","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 0, 0, 1, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 0, 0, 1, 0], [[0, 3], [1, 2], [1, 4], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 0, 0, 1, 0], [[0, 3], [1, 2], [1, 4], [2, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166013,"parameters":{"n":5,"m":2,"images":[1,0,0,1,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,0,0,1,0],\"m\":2,\"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-r06-injective-0014","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 1, 0, 1, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 1, 0, 1, 0], [[0, 2], [0, 4], [1, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([0, 1, 0, 1, 0], [[0, 2], [0, 4], [1, 3], [2, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166014,"parameters":{"n":5,"m":2,"images":[0,1,0,1,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,1,0,1,0],\"m\":2,\"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-r06-injective-0015","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 1, 0, 1, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 1, 0, 1, 0], [[0, 1], [0, 3], [1, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 1, 0, 1, 0], [[0, 1], [0, 3], [1, 3], [2, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166015,"parameters":{"n":5,"m":2,"images":[1,1,0,1,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,1,0,1,0],\"m\":2,\"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-r06-injective-0016","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 0, 1, 1, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 0, 1, 1, 0], [[0, 1], [0, 4], [1, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 1, 0], [[0, 1], [0, 4], [1, 4], [2, 3]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166016,"parameters":{"n":5,"m":2,"images":[0,0,1,1,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,0,1,1,0],\"m\":2,\"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-r06-injective-0017","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 0, 1, 1, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 0, 1, 1, 0], [[0, 2], [0, 3], [1, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 0, 1, 1, 0], [[0, 2], [0, 3], [1, 4], [2, 3]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166017,"parameters":{"n":5,"m":2,"images":[1,0,1,1,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,0,1,1,0],\"m\":2,\"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-r06-injective-0018","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 1, 1, 1, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 1, 1, 1, 0], [[0, 4], [1, 2], [1, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([0, 1, 1, 1, 0], [[0, 4], [1, 2], [1, 3], [2, 3]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166018,"parameters":{"n":5,"m":2,"images":[0,1,1,1,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,1,1,1,0],\"m\":2,\"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-r06-injective-0019","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 1, 1, 1, 0]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 1, 1, 1, 0], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 1, 1, 1, 0], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166019,"parameters":{"n":5,"m":2,"images":[1,1,1,1,0],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,1,1,1,0],\"m\":2,\"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-r06-injective-0020","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 0, 0, 0, 1]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([0, 0, 0, 0, 1], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166020,"parameters":{"n":5,"m":2,"images":[0,0,0,0,1],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,0,0,0,1],\"m\":2,\"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-r06-injective-0021","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 0, 0, 0, 1]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [[0, 4], [1, 2], [1, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 0, 0, 0, 1], [[0, 4], [1, 2], [1, 3], [2, 3]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166021,"parameters":{"n":5,"m":2,"images":[1,0,0,0,1],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,0,0,0,1],\"m\":2,\"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-r06-injective-0022","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 1, 0, 0, 1]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [[0, 2], [0, 3], [1, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([0, 1, 0, 0, 1], [[0, 2], [0, 3], [1, 4], [2, 3]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166022,"parameters":{"n":5,"m":2,"images":[0,1,0,0,1],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,1,0,0,1],\"m\":2,\"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-r06-injective-0023","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 1, 0, 0, 1]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [[0, 1], [0, 4], [1, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 1, 0, 0, 1], [[0, 1], [0, 4], [1, 4], [2, 3]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166023,"parameters":{"n":5,"m":2,"images":[1,1,0,0,1],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,1,0,0,1],\"m\":2,\"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-r06-injective-0024","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[0, 0, 1, 0, 1]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [[0, 1], [0, 3], [1, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 0, 1], [[0, 1], [0, 3], [1, 3], [2, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166024,"parameters":{"n":5,"m":2,"images":[0,0,1,0,1],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[0,0,1,0,1],\"m\":2,\"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-r06-injective-0025","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"完整表的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(5)=[0, 1, 2, 3, 4]→Fin(2)=[0, 1]，images=[1, 0, 1, 0, 1]。求 (原images, 所有x<x2且輸出相同的碰撞對, 單射資格)，碰撞對按原輸入字典序。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], [[0, 2], [0, 4], [1, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 0, 1, 0, 1], [[0, 2], [0, 4], [1, 3], [2, 4]], 否)。全表先合型，再逐對枚舉不同輸入的相等輸出；空碰撞列即單射。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":["完整表的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-all-collision-pairs","seed":202610166025,"parameters":{"n":5,"m":2,"images":[1,0,1,0,1],"domain":"Fin_total_table","operation":"inj-all-collision-pairs","semantic_template":"qf-density16-inj-all-collision-pairs/{\"images\":[1,0,1,0,1],\"m\":2,\"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-r06-injective-0026","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0], [], [], [], 是)","explanation_zh":"有限結構核對=([0], [], [], [], 是)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166026,"parameters":{"n":1,"m":1,"images":[0],"at":0,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0027","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","stem_zh":"Fin型別從0起，完整總表；Fin(3)=[0, 1, 2]→Fin(2)=[0, 1]，images=[0, 0, 1]。刪原輸入at=0，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 0, 1], [[0, 1]], [1, 2], [], 是)","explanation_zh":"有限結構核對=([0, 0, 1], [[0, 1]], [1, 2], [], 是)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166027,"parameters":{"n":3,"m":2,"images":[0,0,1],"at":0,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"at\":0,\"images\":[0,0,1],\"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-r06-injective-0028","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","stem_zh":"Fin型別從0起，完整總表；Fin(4)=[0, 1, 2, 3]→Fin(2)=[0, 1]，images=[0, 0, 1, 1]。刪原輸入at=0，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 0, 1, 1], [[0, 1], [2, 3]], [1, 2, 3], [[2, 3]], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 1], [[0, 1], [2, 3]], [1, 2, 3], [[2, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166028,"parameters":{"n":4,"m":2,"images":[0,0,1,1],"at":0,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"at\":0,\"images\":[0,0,1,1],\"m\":2,\"n\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0029","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]], [1, 2, 3, 4], [[1, 2], [1, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([0, 0, 0, 0, 1], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]], [1, 2, 3, 4], [[1, 2], [1, 3], [2, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166029,"parameters":{"n":5,"m":3,"images":[0,0,0,0,1],"at":0,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0030","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [[0, 4], [1, 2], [1, 3], [2, 3]], [0, 2, 3, 4], [[0, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 0, 0, 0, 1], [[0, 4], [1, 2], [1, 3], [2, 3]], [0, 2, 3, 4], [[0, 4], [2, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166030,"parameters":{"n":5,"m":3,"images":[1,0,0,0,1],"at":1,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0031","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([2, 0, 0, 0, 1], [[1, 2], [1, 3], [2, 3]], [0, 1, 3, 4], [[1, 3]], 否)","explanation_zh":"有限結構核對=([2, 0, 0, 0, 1], [[1, 2], [1, 3], [2, 3]], [0, 1, 3, 4], [[1, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166031,"parameters":{"n":5,"m":3,"images":[2,0,0,0,1],"at":2,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0032","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [[0, 2], [0, 3], [1, 4], [2, 3]], [0, 1, 2, 4], [[0, 2], [1, 4]], 否)","explanation_zh":"有限結構核對=([0, 1, 0, 0, 1], [[0, 2], [0, 3], [1, 4], [2, 3]], [0, 1, 2, 4], [[0, 2], [1, 4]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166032,"parameters":{"n":5,"m":3,"images":[0,1,0,0,1],"at":3,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0033","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [[0, 1], [0, 4], [1, 4], [2, 3]], [0, 1, 2, 3], [[0, 1], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 1, 0, 0, 1], [[0, 1], [0, 4], [1, 4], [2, 3]], [0, 1, 2, 3], [[0, 1], [2, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166033,"parameters":{"n":5,"m":3,"images":[1,1,0,0,1],"at":4,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0034","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([2, 1, 0, 0, 1], [[1, 4], [2, 3]], [1, 2, 3, 4], [[1, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([2, 1, 0, 0, 1], [[1, 4], [2, 3]], [1, 2, 3, 4], [[1, 4], [2, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166034,"parameters":{"n":5,"m":3,"images":[2,1,0,0,1],"at":0,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0035","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 2, 0, 0, 1], [[0, 2], [0, 3], [2, 3]], [0, 2, 3, 4], [[0, 2], [0, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([0, 2, 0, 0, 1], [[0, 2], [0, 3], [2, 3]], [0, 2, 3, 4], [[0, 2], [0, 3], [2, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166035,"parameters":{"n":5,"m":3,"images":[0,2,0,0,1],"at":1,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0036","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([1, 2, 0, 0, 1], [[0, 4], [2, 3]], [0, 1, 3, 4], [[0, 4]], 否)","explanation_zh":"有限結構核對=([1, 2, 0, 0, 1], [[0, 4], [2, 3]], [0, 1, 3, 4], [[0, 4]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166036,"parameters":{"n":5,"m":3,"images":[1,2,0,0,1],"at":2,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0037","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([2, 2, 0, 0, 1], [[0, 1], [2, 3]], [0, 1, 2, 4], [[0, 1]], 否)","explanation_zh":"有限結構核對=([2, 2, 0, 0, 1], [[0, 1], [2, 3]], [0, 1, 2, 4], [[0, 1]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166037,"parameters":{"n":5,"m":3,"images":[2,2,0,0,1],"at":3,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0038","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [[0, 1], [0, 3], [1, 3], [2, 4]], [0, 1, 2, 3], [[0, 1], [0, 3], [1, 3]], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 0, 1], [[0, 1], [0, 3], [1, 3], [2, 4]], [0, 1, 2, 3], [[0, 1], [0, 3], [1, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166038,"parameters":{"n":5,"m":3,"images":[0,0,1,0,1],"at":4,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0039","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], [[0, 2], [0, 4], [1, 3], [2, 4]], [1, 2, 3, 4], [[1, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 0, 1, 0, 1], [[0, 2], [0, 4], [1, 3], [2, 4]], [1, 2, 3, 4], [[1, 3], [2, 4]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166039,"parameters":{"n":5,"m":3,"images":[1,0,1,0,1],"at":0,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0040","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([2, 0, 1, 0, 1], [[1, 3], [2, 4]], [0, 2, 3, 4], [[2, 4]], 否)","explanation_zh":"有限結構核對=([2, 0, 1, 0, 1], [[1, 3], [2, 4]], [0, 2, 3, 4], [[2, 4]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166040,"parameters":{"n":5,"m":3,"images":[2,0,1,0,1],"at":1,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0041","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 1], [[0, 3], [1, 2], [1, 4], [2, 4]], [0, 1, 3, 4], [[0, 3], [1, 4]], 否)","explanation_zh":"有限結構核對=([0, 1, 1, 0, 1], [[0, 3], [1, 2], [1, 4], [2, 4]], [0, 1, 3, 4], [[0, 3], [1, 4]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166041,"parameters":{"n":5,"m":3,"images":[0,1,1,0,1],"at":2,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0042","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 1], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], [0, 1, 2, 4], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 1, 1, 0, 1], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], [0, 1, 2, 4], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166042,"parameters":{"n":5,"m":3,"images":[1,1,1,0,1],"at":3,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0043","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([2, 1, 1, 0, 1], [[1, 2], [1, 4], [2, 4]], [0, 1, 2, 3], [[1, 2]], 否)","explanation_zh":"有限結構核對=([2, 1, 1, 0, 1], [[1, 2], [1, 4], [2, 4]], [0, 1, 2, 3], [[1, 2]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166043,"parameters":{"n":5,"m":3,"images":[2,1,1,0,1],"at":4,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0044","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 2, 1, 0, 1], [[0, 3], [2, 4]], [1, 2, 3, 4], [[2, 4]], 否)","explanation_zh":"有限結構核對=([0, 2, 1, 0, 1], [[0, 3], [2, 4]], [1, 2, 3, 4], [[2, 4]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166044,"parameters":{"n":5,"m":3,"images":[0,2,1,0,1],"at":0,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0045","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([1, 2, 1, 0, 1], [[0, 2], [0, 4], [2, 4]], [0, 2, 3, 4], [[0, 2], [0, 4], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 2, 1, 0, 1], [[0, 2], [0, 4], [2, 4]], [0, 2, 3, 4], [[0, 2], [0, 4], [2, 4]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166045,"parameters":{"n":5,"m":3,"images":[1,2,1,0,1],"at":1,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0046","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([2, 2, 1, 0, 1], [[0, 1], [2, 4]], [0, 1, 3, 4], [[0, 1]], 否)","explanation_zh":"有限結構核對=([2, 2, 1, 0, 1], [[0, 1], [2, 4]], [0, 1, 3, 4], [[0, 1]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166046,"parameters":{"n":5,"m":3,"images":[2,2,1,0,1],"at":2,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0047","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 0, 2, 0, 1], [[0, 1], [0, 3], [1, 3]], [0, 1, 2, 4], [[0, 1]], 否)","explanation_zh":"有限結構核對=([0, 0, 2, 0, 1], [[0, 1], [0, 3], [1, 3]], [0, 1, 2, 4], [[0, 1]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166047,"parameters":{"n":5,"m":3,"images":[0,0,2,0,1],"at":3,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0048","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([1, 0, 2, 0, 1], [[0, 4], [1, 3]], [0, 1, 2, 3], [[1, 3]], 否)","explanation_zh":"有限結構核對=([1, 0, 2, 0, 1], [[0, 4], [1, 3]], [0, 1, 2, 3], [[1, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166048,"parameters":{"n":5,"m":3,"images":[1,0,2,0,1],"at":4,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0049","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([2, 0, 2, 0, 1], [[0, 2], [1, 3]], [1, 2, 3, 4], [[1, 3]], 否)","explanation_zh":"有限結構核對=([2, 0, 2, 0, 1], [[0, 2], [1, 3]], [1, 2, 3, 4], [[1, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166049,"parameters":{"n":5,"m":3,"images":[2,0,2,0,1],"at":0,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0050","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"刪一輸入的碰撞變化","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，陪域不變。求 (原images, 原碰撞, 保留原始輸入標籤, 刪後碰撞, 刪後單射資格)，不重編輸入索引。","answer":{"kind":"expression","value":"([0, 1, 2, 0, 1], [[0, 3], [1, 4]], [0, 2, 3, 4], [[0, 3]], 否)","explanation_zh":"有限結構核對=([0, 1, 2, 0, 1], [[0, 3], [1, 4]], [0, 2, 3, 4], [[0, 3]], 否)。只移去該原始標籤，完整碰撞比較仍使用保留的原始輸入標籤。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":["刪一輸入的碰撞變化"]},"variant":{"family_id":"qf-density16-inj-remove-input-collision-change","seed":202610166050,"parameters":{"n":5,"m":3,"images":[0,1,2,0,1],"at":1,"domain":"Fin_total_table","operation":"inj-remove-input-collision-change","semantic_template":"qf-density16-inj-remove-input-collision-change/{\"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-r06-injective-0051","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(0)=∅，images=[]。在新輸入標籤n附加候選value=0。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([], 否, 不合陪域, 不求值, 不求值)","explanation_zh":"有限結構核對=([], 否, 不合陪域, 不求值, 不求值)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166051,"parameters":{"n":0,"m":0,"images":[],"value":0,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[],\"m\":0,\"n\":0,\"value\":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-r06-injective-0052","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(1)=[0]，images=[]。在新輸入標籤n附加候選value=0。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([], 是, [0], [], 是)","explanation_zh":"有限結構核對=([], 是, [0], [], 是)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166052,"parameters":{"n":0,"m":1,"images":[],"value":0,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[],\"m\":1,\"n\":0,\"value\":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-r06-injective-0053","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","stem_zh":"Fin型別從0起，完整總表；Fin(2)=[0, 1]→Fin(3)=[0, 1, 2]，images=[0, 1]。在新輸入標籤n附加候選value=2。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 1], 是, [0, 1, 2], [], 是)","explanation_zh":"有限結構核對=([0, 1], 是, [0, 1, 2], [], 是)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166053,"parameters":{"n":2,"m":3,"images":[0,1],"value":2,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,1],\"m\":3,\"n\":2,\"value\":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-r06-injective-0054","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","stem_zh":"Fin型別從0起，完整總表；Fin(2)=[0, 1]→Fin(2)=[0, 1]，images=[0, 1]。在新輸入標籤n附加候選value=0。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 1], 是, [0, 1, 0], [[0, 2]], 否)","explanation_zh":"有限結構核對=([0, 1], 是, [0, 1, 0], [[0, 2]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166054,"parameters":{"n":2,"m":2,"images":[0,1],"value":0,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,1],\"m\":2,\"n\":2,\"value\":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-r06-injective-0055","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","stem_zh":"Fin型別從0起，完整總表；Fin(2)=[0, 1]→Fin(2)=[0, 1]，images=[0, 1]。在新輸入標籤n附加候選value=-1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 1], 否, 不合陪域, 不求值, 不求值)","explanation_zh":"有限結構核對=([0, 1], 否, 不合陪域, 不求值, 不求值)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166055,"parameters":{"n":2,"m":2,"images":[0,1],"value":-1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,1],\"m\":2,\"n\":2,\"value\":-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-r06-injective-0056","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","stem_zh":"Fin型別從0起，完整總表；Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]→Fin(8)=[0, 1, 2, 3, 4, 5, 6, 7]，images=[0, 1, 2, 3, 4, 5, 6, 7]。在新輸入標籤n附加候選value=7。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7], 是, [0, 1, 2, 3, 4, 5, 6, 7, 7], [[7, 8]], 否)","explanation_zh":"有限結構核對=([0, 1, 2, 3, 4, 5, 6, 7], 是, [0, 1, 2, 3, 4, 5, 6, 7, 7], [[7, 8]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166056,"parameters":{"n":8,"m":8,"images":[0,1,2,3,4,5,6,7],"value":7,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,1,2,3,4,5,6,7],\"m\":8,\"n\":8,\"value\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0057","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], 是, [0, 0, 0, 0, 1, 1], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3], [4, 5]], 否)","explanation_zh":"有限結構核對=([0, 0, 0, 0, 1], 是, [0, 0, 0, 0, 1, 1], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3], [4, 5]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166057,"parameters":{"n":5,"m":3,"images":[0,0,0,0,1],"value":1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,0,0,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0058","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=2。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], 是, [1, 0, 0, 0, 1, 2], [[0, 4], [1, 2], [1, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 0, 0, 0, 1], 是, [1, 0, 0, 0, 1, 2], [[0, 4], [1, 2], [1, 3], [2, 3]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166058,"parameters":{"n":5,"m":3,"images":[1,0,0,0,1],"value":2,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[1,0,0,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0059","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=-1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([2, 0, 0, 0, 1], 否, 不合陪域, 不求值, 不求值)","explanation_zh":"有限結構核對=([2, 0, 0, 0, 1], 否, 不合陪域, 不求值, 不求值)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166059,"parameters":{"n":5,"m":3,"images":[2,0,0,0,1],"value":-1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[2,0,0,0,1],\"m\":3,\"n\":5,\"value\":-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-r06-injective-0060","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=0。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], 是, [0, 1, 0, 0, 1, 0], [[0, 2], [0, 3], [0, 5], [1, 4], [2, 3], [2, 5], [3, 5]], 否)","explanation_zh":"有限結構核對=([0, 1, 0, 0, 1], 是, [0, 1, 0, 0, 1, 0], [[0, 2], [0, 3], [0, 5], [1, 4], [2, 3], [2, 5], [3, 5]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166060,"parameters":{"n":5,"m":3,"images":[0,1,0,0,1],"value":0,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,1,0,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0061","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], 是, [1, 1, 0, 0, 1, 1], [[0, 1], [0, 4], [0, 5], [1, 4], [1, 5], [2, 3], [4, 5]], 否)","explanation_zh":"有限結構核對=([1, 1, 0, 0, 1], 是, [1, 1, 0, 0, 1, 1], [[0, 1], [0, 4], [0, 5], [1, 4], [1, 5], [2, 3], [4, 5]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166061,"parameters":{"n":5,"m":3,"images":[1,1,0,0,1],"value":1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[1,1,0,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0062","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=2。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([2, 1, 0, 0, 1], 是, [2, 1, 0, 0, 1, 2], [[0, 5], [1, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([2, 1, 0, 0, 1], 是, [2, 1, 0, 0, 1, 2], [[0, 5], [1, 4], [2, 3]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166062,"parameters":{"n":5,"m":3,"images":[2,1,0,0,1],"value":2,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[2,1,0,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0063","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=-1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 2, 0, 0, 1], 否, 不合陪域, 不求值, 不求值)","explanation_zh":"有限結構核對=([0, 2, 0, 0, 1], 否, 不合陪域, 不求值, 不求值)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166063,"parameters":{"n":5,"m":3,"images":[0,2,0,0,1],"value":-1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,2,0,0,1],\"m\":3,\"n\":5,\"value\":-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-r06-injective-0064","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=0。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([1, 2, 0, 0, 1], 是, [1, 2, 0, 0, 1, 0], [[0, 4], [2, 3], [2, 5], [3, 5]], 否)","explanation_zh":"有限結構核對=([1, 2, 0, 0, 1], 是, [1, 2, 0, 0, 1, 0], [[0, 4], [2, 3], [2, 5], [3, 5]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166064,"parameters":{"n":5,"m":3,"images":[1,2,0,0,1],"value":0,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[1,2,0,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0065","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([2, 2, 0, 0, 1], 是, [2, 2, 0, 0, 1, 1], [[0, 1], [2, 3], [4, 5]], 否)","explanation_zh":"有限結構核對=([2, 2, 0, 0, 1], 是, [2, 2, 0, 0, 1, 1], [[0, 1], [2, 3], [4, 5]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166065,"parameters":{"n":5,"m":3,"images":[2,2,0,0,1],"value":1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[2,2,0,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0066","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=2。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], 是, [0, 0, 1, 0, 1, 2], [[0, 1], [0, 3], [1, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 0, 1], 是, [0, 0, 1, 0, 1, 2], [[0, 1], [0, 3], [1, 3], [2, 4]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166066,"parameters":{"n":5,"m":3,"images":[0,0,1,0,1],"value":2,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,0,1,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0067","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=-1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], 否, 不合陪域, 不求值, 不求值)","explanation_zh":"有限結構核對=([1, 0, 1, 0, 1], 否, 不合陪域, 不求值, 不求值)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166067,"parameters":{"n":5,"m":3,"images":[1,0,1,0,1],"value":-1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[1,0,1,0,1],\"m\":3,\"n\":5,\"value\":-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-r06-injective-0068","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=0。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([2, 0, 1, 0, 1], 是, [2, 0, 1, 0, 1, 0], [[1, 3], [1, 5], [2, 4], [3, 5]], 否)","explanation_zh":"有限結構核對=([2, 0, 1, 0, 1], 是, [2, 0, 1, 0, 1, 0], [[1, 3], [1, 5], [2, 4], [3, 5]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166068,"parameters":{"n":5,"m":3,"images":[2,0,1,0,1],"value":0,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[2,0,1,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0069","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 1], 是, [0, 1, 1, 0, 1, 1], [[0, 3], [1, 2], [1, 4], [1, 5], [2, 4], [2, 5], [4, 5]], 否)","explanation_zh":"有限結構核對=([0, 1, 1, 0, 1], 是, [0, 1, 1, 0, 1, 1], [[0, 3], [1, 2], [1, 4], [1, 5], [2, 4], [2, 5], [4, 5]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166069,"parameters":{"n":5,"m":3,"images":[0,1,1,0,1],"value":1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,1,1,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0070","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=2。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 1], 是, [1, 1, 1, 0, 1, 2], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 1, 1, 0, 1], 是, [1, 1, 1, 0, 1, 2], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166070,"parameters":{"n":5,"m":3,"images":[1,1,1,0,1],"value":2,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[1,1,1,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0071","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=-1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([2, 1, 1, 0, 1], 否, 不合陪域, 不求值, 不求值)","explanation_zh":"有限結構核對=([2, 1, 1, 0, 1], 否, 不合陪域, 不求值, 不求值)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166071,"parameters":{"n":5,"m":3,"images":[2,1,1,0,1],"value":-1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[2,1,1,0,1],\"m\":3,\"n\":5,\"value\":-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-r06-injective-0072","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=0。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 2, 1, 0, 1], 是, [0, 2, 1, 0, 1, 0], [[0, 3], [0, 5], [2, 4], [3, 5]], 否)","explanation_zh":"有限結構核對=([0, 2, 1, 0, 1], 是, [0, 2, 1, 0, 1, 0], [[0, 3], [0, 5], [2, 4], [3, 5]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166072,"parameters":{"n":5,"m":3,"images":[0,2,1,0,1],"value":0,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,2,1,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0073","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([1, 2, 1, 0, 1], 是, [1, 2, 1, 0, 1, 1], [[0, 2], [0, 4], [0, 5], [2, 4], [2, 5], [4, 5]], 否)","explanation_zh":"有限結構核對=([1, 2, 1, 0, 1], 是, [1, 2, 1, 0, 1, 1], [[0, 2], [0, 4], [0, 5], [2, 4], [2, 5], [4, 5]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166073,"parameters":{"n":5,"m":3,"images":[1,2,1,0,1],"value":1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[1,2,1,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0074","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=2。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([2, 2, 1, 0, 1], 是, [2, 2, 1, 0, 1, 2], [[0, 1], [0, 5], [1, 5], [2, 4]], 否)","explanation_zh":"有限結構核對=([2, 2, 1, 0, 1], 是, [2, 2, 1, 0, 1, 2], [[0, 1], [0, 5], [1, 5], [2, 4]], 否)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166074,"parameters":{"n":5,"m":3,"images":[2,2,1,0,1],"value":2,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[2,2,1,0,1],\"m\":3,\"n\":5,\"value\":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-r06-injective-0075","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"附加輸出的陪域資格","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]。在新輸入標籤n附加候選value=-1。求 (原images, 新值陪域資格, 新images或不合陪域, 新碰撞或不求值, 新單射資格或不求值)。合格附加可使新域有9標籤。","answer":{"kind":"expression","value":"([0, 0, 2, 0, 1], 否, 不合陪域, 不求值, 不求值)","explanation_zh":"有限結構核對=([0, 0, 2, 0, 1], 否, 不合陪域, 不求值, 不求值)。候選先落在原陪域才附加新格並枚舉碰撞；域外不造新表或性質。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":["附加輸出的陪域資格"]},"variant":{"family_id":"qf-density16-inj-append-output-qualification","seed":202610166075,"parameters":{"n":5,"m":3,"images":[0,0,2,0,1],"value":-1,"domain":"Fin_total_table","operation":"inj-append-output-qualification","semantic_template":"qf-density16-inj-append-output-qualification/{\"images\":[0,0,2,0,1],\"m\":3,\"n\":5,\"value\":-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-r06-injective-0076","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","stem_zh":"Fin型別從0起，完整總表；Fin(0)=∅→Fin(0)=∅，images=[]。原序subset=[]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([], [], [], 是)","explanation_zh":"有限結構核對=([], [], [], 是)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166076,"parameters":{"n":0,"m":0,"images":[],"subset":[],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[],\"m\":0,\"n\":0,\"subset\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，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-r06-injective-0077","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[2, 0]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 0, 1], [0, 2], [], 是)","explanation_zh":"有限結構核對=([0, 0, 1], [0, 2], [], 是)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166077,"parameters":{"n":3,"m":2,"images":[0,0,1],"subset":[2,0],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,0,1],\"m\":2,\"n\":3,\"subset\":[0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0078","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[1, 0]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 0, 1], [0, 1], [[0, 1]], 否)","explanation_zh":"有限結構核對=([0, 0, 1], [0, 1], [[0, 1]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166078,"parameters":{"n":3,"m":2,"images":[0,0,1],"subset":[1,0],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,0,1],\"m\":2,\"n\":3,\"subset\":[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-r06-injective-0079","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 0, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([0, 0, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166079,"parameters":{"n":5,"m":3,"images":[0,0,0,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,0,0,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0080","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([1, 0, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 4], [1, 2], [1, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 0, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 4], [1, 2], [1, 3], [2, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166080,"parameters":{"n":5,"m":3,"images":[1,0,0,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[1,0,0,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0081","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([2, 0, 0, 0, 1], [0, 1, 2, 3, 4], [[1, 2], [1, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([2, 0, 0, 0, 1], [0, 1, 2, 3, 4], [[1, 2], [1, 3], [2, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166081,"parameters":{"n":5,"m":3,"images":[2,0,0,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[2,0,0,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0082","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 1, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [0, 3], [1, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([0, 1, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [0, 3], [1, 4], [2, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166082,"parameters":{"n":5,"m":3,"images":[0,1,0,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,1,0,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0083","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([1, 1, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 4], [1, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 1, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 4], [1, 4], [2, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166083,"parameters":{"n":5,"m":3,"images":[1,1,0,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[1,1,0,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0084","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([2, 1, 0, 0, 1], [0, 1, 2, 3, 4], [[1, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([2, 1, 0, 0, 1], [0, 1, 2, 3, 4], [[1, 4], [2, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166084,"parameters":{"n":5,"m":3,"images":[2,1,0,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[2,1,0,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0085","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 2, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [0, 3], [2, 3]], 否)","explanation_zh":"有限結構核對=([0, 2, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [0, 3], [2, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166085,"parameters":{"n":5,"m":3,"images":[0,2,0,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,2,0,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0086","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([1, 2, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 4], [2, 3]], 否)","explanation_zh":"有限結構核對=([1, 2, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 4], [2, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166086,"parameters":{"n":5,"m":3,"images":[1,2,0,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[1,2,0,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0087","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([2, 2, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [2, 3]], 否)","explanation_zh":"有限結構核對=([2, 2, 0, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [2, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166087,"parameters":{"n":5,"m":3,"images":[2,2,0,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[2,2,0,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0088","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 0, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 3], [1, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([0, 0, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 3], [1, 3], [2, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166088,"parameters":{"n":5,"m":3,"images":[0,0,1,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,0,1,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0089","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([1, 0, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [0, 4], [1, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 0, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [0, 4], [1, 3], [2, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166089,"parameters":{"n":5,"m":3,"images":[1,0,1,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[1,0,1,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0090","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([2, 0, 1, 0, 1], [0, 1, 2, 3, 4], [[1, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([2, 0, 1, 0, 1], [0, 1, 2, 3, 4], [[1, 3], [2, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166090,"parameters":{"n":5,"m":3,"images":[2,0,1,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[2,0,1,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0091","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 1, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 3], [1, 2], [1, 4], [2, 4]], 否)","explanation_zh":"有限結構核對=([0, 1, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 3], [1, 2], [1, 4], [2, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166091,"parameters":{"n":5,"m":3,"images":[0,1,1,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,1,1,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0092","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([1, 1, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 1, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 2], [0, 4], [1, 2], [1, 4], [2, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166092,"parameters":{"n":5,"m":3,"images":[1,1,1,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[1,1,1,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0093","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([2, 1, 1, 0, 1], [0, 1, 2, 3, 4], [[1, 2], [1, 4], [2, 4]], 否)","explanation_zh":"有限結構核對=([2, 1, 1, 0, 1], [0, 1, 2, 3, 4], [[1, 2], [1, 4], [2, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166093,"parameters":{"n":5,"m":3,"images":[2,1,1,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[2,1,1,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0094","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 2, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 3], [2, 4]], 否)","explanation_zh":"有限結構核對=([0, 2, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 3], [2, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166094,"parameters":{"n":5,"m":3,"images":[0,2,1,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,2,1,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0095","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([1, 2, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [0, 4], [2, 4]], 否)","explanation_zh":"有限結構核對=([1, 2, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [0, 4], [2, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166095,"parameters":{"n":5,"m":3,"images":[1,2,1,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[1,2,1,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0096","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([2, 2, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [2, 4]], 否)","explanation_zh":"有限結構核對=([2, 2, 1, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [2, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166096,"parameters":{"n":5,"m":3,"images":[2,2,1,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[2,2,1,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0097","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 0, 2, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 3], [1, 3]], 否)","explanation_zh":"有限結構核對=([0, 0, 2, 0, 1], [0, 1, 2, 3, 4], [[0, 1], [0, 3], [1, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166097,"parameters":{"n":5,"m":3,"images":[0,0,2,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,0,2,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0098","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([1, 0, 2, 0, 1], [0, 1, 2, 3, 4], [[0, 4], [1, 3]], 否)","explanation_zh":"有限結構核對=([1, 0, 2, 0, 1], [0, 1, 2, 3, 4], [[0, 4], [1, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166098,"parameters":{"n":5,"m":3,"images":[1,0,2,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[1,0,2,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0099","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([2, 0, 2, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [1, 3]], 否)","explanation_zh":"有限結構核對=([2, 0, 2, 0, 1], [0, 1, 2, 3, 4], [[0, 2], [1, 3]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166099,"parameters":{"n":5,"m":3,"images":[2,0,2,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[2,0,2,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261012-advance-20261016-r06-injective-0100","batch_id":"batch-20261012-advance-20261016-r06-injective-foundations","language":"zh-Hant","source_mko_ids":["mko-injective"],"title_zh":"子域限制的全部碰撞","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]。原序subset=[4, 2, 0, 1, 3]，已宣告為無重複合法來源標籤。求 (原images, 排序subset, 子域內全部碰撞, 限制單射資格)。","answer":{"kind":"expression","value":"([0, 1, 2, 0, 1], [0, 1, 2, 3, 4], [[0, 3], [1, 4]], 否)","explanation_zh":"有限結構核對=([0, 1, 2, 0, 1], [0, 1, 2, 3, 4], [[0, 3], [1, 4]], 否)。先驗完整原表，再只比較子域標籤；排序不把不同輸入合併。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":["子域限制的全部碰撞"]},"variant":{"family_id":"qf-density16-inj-restriction-subset-witness","seed":202610166100,"parameters":{"n":5,"m":3,"images":[0,1,2,0,1],"subset":[4,2,0,1,3],"domain":"Fin_total_table","operation":"inj-restriction-subset-witness","semantic_template":"qf-density16-inj-restriction-subset-witness/{\"images\":[0,1,2,0,1],\"m\":3,\"n\":5,\"subset\":[0,1,2,3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_integer_rational_arithmetic","producer_finite_enumeration","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-12","contract_version":"ocme-question-factory-v0.1"}}