{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0001","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225001,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0002","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 0, 3, 4, 1], [0, 1, 2, 3, 4], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 0, 3, 4, 1], [0, 1, 2, 3, 4], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225002,"parameters":{"n":5,"table":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0003","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 3, 0, 4, 2], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [4, 2, 3, 0, 1], [2, 0, 4, 1, 3]], 是)","explanation_zh":"結構基礎核對=(5, [[1, 3, 0, 4, 2], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [4, 2, 3, 0, 1], [2, 0, 4, 1, 3]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225003,"parameters":{"n":5,"table":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0004","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 2, 4, 0, 3], [2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [0, 1, 2, 3, 4], [3, 0, 1, 4, 2]], 是)","explanation_zh":"結構基礎核對=(5, [[1, 2, 4, 0, 3], [2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [0, 1, 2, 3, 4], [3, 0, 1, 4, 2]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225004,"parameters":{"n":5,"table":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0005","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4]], 是)","explanation_zh":"結構基礎核對=(5, [[1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225005,"parameters":{"n":5,"table":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0006","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [4, 2, 0, 1, 3]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [4, 2, 0, 1, 3]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225006,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0007","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 0, 3, 1, 2], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 0, 3, 1, 2], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225007,"parameters":{"n":5,"table":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0008","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [2, 4, 3, 1, 0], [1, 2, 4, 0, 3]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [2, 4, 3, 1, 0], [1, 2, 4, 0, 3]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225008,"parameters":{"n":5,"table":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0009","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 2, 3, 0, 1], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [1, 3, 0, 4, 2]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 2, 3, 0, 1], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [1, 3, 0, 4, 2]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225009,"parameters":{"n":5,"table":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0010","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 2, 4, 1, 0], [2, 0, 3, 4, 1], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 2, 4, 1, 0], [2, 0, 3, 4, 1], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225010,"parameters":{"n":5,"table":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0011","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 4, 0, 2, 3], [2, 0, 3, 4, 1], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 4, 0, 2, 3], [2, 0, 3, 4, 1], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225011,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0012","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225012,"parameters":{"n":5,"table":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0013","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [3, 0, 4, 2, 1]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [3, 0, 4, 2, 1]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225013,"parameters":{"n":5,"table":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0014","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 3, 1, 0, 2], [3, 2, 4, 1, 0], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4], [2, 0, 3, 4, 1]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 3, 1, 0, 2], [3, 2, 4, 1, 0], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4], [2, 0, 3, 4, 1]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225014,"parameters":{"n":5,"table":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0015","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 4, 1, 2, 0], [4, 2, 3, 0, 1], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [0, 1, 2, 3, 4]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 4, 1, 2, 0], [4, 2, 3, 0, 1], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [0, 1, 2, 3, 4]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225015,"parameters":{"n":5,"table":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0016","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [4, 2, 3, 0, 1]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [4, 2, 3, 0, 1]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225016,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0017","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [1, 2, 4, 0, 3], [4, 3, 0, 2, 1], [2, 4, 3, 1, 0]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [1, 2, 4, 0, 3], [4, 3, 0, 2, 1], [2, 4, 3, 1, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225017,"parameters":{"n":5,"table":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0018","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 2, 0, 4, 1], [2, 4, 1, 0, 3], [0, 1, 2, 3, 4], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 2, 0, 4, 1], [2, 4, 1, 0, 3], [0, 1, 2, 3, 4], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225018,"parameters":{"n":5,"table":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0019","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225019,"parameters":{"n":5,"table":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0020","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [1, 2, 4, 0, 3], [0, 1, 2, 3, 4]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [1, 2, 4, 0, 3], [0, 1, 2, 3, 4]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225020,"parameters":{"n":5,"table":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0021","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3], [3, 2, 0, 4, 1], [4, 0, 3, 1, 2]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3], [3, 2, 0, 4, 1], [4, 0, 3, 1, 2]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225021,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0022","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 0, 4, 2, 1], [0, 1, 2, 3, 4], [4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [1, 4, 3, 0, 2]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 0, 4, 2, 1], [0, 1, 2, 3, 4], [4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [1, 4, 3, 0, 2]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225022,"parameters":{"n":5,"table":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0023","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225023,"parameters":{"n":5,"table":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0024","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 4, 1, 0, 3], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 4, 1, 0, 3], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225024,"parameters":{"n":5,"table":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0025","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-table-qualification；資料={\"n\":5,\"table\":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]]}。請依 [n,table,closed] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [1, 4, 3, 0, 2], [4, 2, 0, 1, 3], [0, 1, 2, 3, 4]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [1, 4, 3, 0, 2], [4, 2, 0, 1, 3], [0, 1, 2, 3, 4]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-table-qualification","seed":202610225025,"parameters":{"n":5,"table":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-table-qualification","semantic_template":"qf-str22-group-table-qualification/{\"n\":5,\"table\":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0026","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], [], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225026,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0027","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 0, 3, 4, 1], [0, 1, 2, 3, 4], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3]], [], 是)","explanation_zh":"結構基礎核對=(5, [[2, 0, 3, 4, 1], [0, 1, 2, 3, 4], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225027,"parameters":{"n":5,"table":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0028","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 3, 0, 4, 2], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [4, 2, 3, 0, 1], [2, 0, 4, 1, 3]], [], 是)","explanation_zh":"結構基礎核對=(5, [[1, 3, 0, 4, 2], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [4, 2, 3, 0, 1], [2, 0, 4, 1, 3]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225028,"parameters":{"n":5,"table":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0029","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 2, 4, 0, 3], [2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [0, 1, 2, 3, 4], [3, 0, 1, 4, 2]], [], 是)","explanation_zh":"結構基礎核對=(5, [[1, 2, 4, 0, 3], [2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [0, 1, 2, 3, 4], [3, 0, 1, 4, 2]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225029,"parameters":{"n":5,"table":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0030","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4]], [], 是)","explanation_zh":"結構基礎核對=(5, [[1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225030,"parameters":{"n":5,"table":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0031","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [4, 2, 0, 1, 3]], [], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [4, 2, 0, 1, 3]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225031,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0032","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 0, 3, 1, 2], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3]], [], 是)","explanation_zh":"結構基礎核對=(5, [[4, 0, 3, 1, 2], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225032,"parameters":{"n":5,"table":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0033","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [2, 4, 3, 1, 0], [1, 2, 4, 0, 3]], [], 是)","explanation_zh":"結構基礎核對=(5, [[4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [2, 4, 3, 1, 0], [1, 2, 4, 0, 3]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225033,"parameters":{"n":5,"table":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0034","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 2, 3, 0, 1], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [1, 3, 0, 4, 2]], [], 是)","explanation_zh":"結構基礎核對=(5, [[4, 2, 3, 0, 1], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [1, 3, 0, 4, 2]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225034,"parameters":{"n":5,"table":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0035","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 2, 4, 1, 0], [2, 0, 3, 4, 1], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4]], [], 是)","explanation_zh":"結構基礎核對=(5, [[3, 2, 4, 1, 0], [2, 0, 3, 4, 1], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225035,"parameters":{"n":5,"table":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0036","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 4, 0, 2, 3], [2, 0, 3, 4, 1], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2]], [], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 4, 0, 2, 3], [2, 0, 3, 4, 1], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225036,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0037","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2]], [], 是)","explanation_zh":"結構基礎核對=(5, [[4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225037,"parameters":{"n":5,"table":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0038","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [3, 0, 4, 2, 1]], [], 是)","explanation_zh":"結構基礎核對=(5, [[4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [3, 0, 4, 2, 1]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225038,"parameters":{"n":5,"table":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0039","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 3, 1, 0, 2], [3, 2, 4, 1, 0], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4], [2, 0, 3, 4, 1]], [], 是)","explanation_zh":"結構基礎核對=(5, [[4, 3, 1, 0, 2], [3, 2, 4, 1, 0], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4], [2, 0, 3, 4, 1]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225039,"parameters":{"n":5,"table":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0040","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 4, 1, 2, 0], [4, 2, 3, 0, 1], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [0, 1, 2, 3, 4]], [], 是)","explanation_zh":"結構基礎核對=(5, [[3, 4, 1, 2, 0], [4, 2, 3, 0, 1], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [0, 1, 2, 3, 4]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225040,"parameters":{"n":5,"table":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0041","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [4, 2, 3, 0, 1]], [], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [4, 2, 3, 0, 1]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225041,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0042","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [1, 2, 4, 0, 3], [4, 3, 0, 2, 1], [2, 4, 3, 1, 0]], [], 是)","explanation_zh":"結構基礎核對=(5, [[3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [1, 2, 4, 0, 3], [4, 3, 0, 2, 1], [2, 4, 3, 1, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225042,"parameters":{"n":5,"table":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0043","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 2, 0, 4, 1], [2, 4, 1, 0, 3], [0, 1, 2, 3, 4], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0]], [], 是)","explanation_zh":"結構基礎核對=(5, [[3, 2, 0, 4, 1], [2, 4, 1, 0, 3], [0, 1, 2, 3, 4], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225043,"parameters":{"n":5,"table":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0044","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0]], [], 是)","explanation_zh":"結構基礎核對=(5, [[2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225044,"parameters":{"n":5,"table":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0045","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [1, 2, 4, 0, 3], [0, 1, 2, 3, 4]], [], 是)","explanation_zh":"結構基礎核對=(5, [[2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [1, 2, 4, 0, 3], [0, 1, 2, 3, 4]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225045,"parameters":{"n":5,"table":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0046","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3], [3, 2, 0, 4, 1], [4, 0, 3, 1, 2]], [], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3], [3, 2, 0, 4, 1], [4, 0, 3, 1, 2]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225046,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0047","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 0, 4, 2, 1], [0, 1, 2, 3, 4], [4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [1, 4, 3, 0, 2]], [], 是)","explanation_zh":"結構基礎核對=(5, [[3, 0, 4, 2, 1], [0, 1, 2, 3, 4], [4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [1, 4, 3, 0, 2]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225047,"parameters":{"n":5,"table":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0048","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1]], [], 是)","explanation_zh":"結構基礎核對=(5, [[3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225048,"parameters":{"n":5,"table":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0049","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 4, 1, 0, 3], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1]], [], 是)","explanation_zh":"結構基礎核對=(5, [[2, 4, 1, 0, 3], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225049,"parameters":{"n":5,"table":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0050","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-associativity-audit；資料={\"n\":5,\"table\":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]]}。請依 [n,table,bad_triples,associative] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [1, 4, 3, 0, 2], [4, 2, 0, 1, 3], [0, 1, 2, 3, 4]], [], 是)","explanation_zh":"結構基礎核對=(5, [[2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [1, 4, 3, 0, 2], [4, 2, 0, 1, 3], [0, 1, 2, 3, 4]], [], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-associativity-audit","seed":202610225050,"parameters":{"n":5,"table":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-associativity-audit","semantic_template":"qf-str22-group-associativity-audit/{\"n\":5,\"table\":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0051","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], [0], [[0, [0]], [1, [4]], [2, [3]], [3, [2]], [4, [1]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], [0], [[0, [0]], [1, [4]], [2, [3]], [3, [2]], [4, [1]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225051,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0052","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 0, 3, 4, 1], [0, 1, 2, 3, 4], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3]], [1], [[0, [4]], [1, [1]], [2, [3]], [3, [2]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 0, 3, 4, 1], [0, 1, 2, 3, 4], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3]], [1], [[0, [4]], [1, [1]], [2, [3]], [3, [2]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225052,"parameters":{"n":5,"table":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0053","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 3, 0, 4, 2], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [4, 2, 3, 0, 1], [2, 0, 4, 1, 3]], [2], [[0, [4]], [1, [3]], [2, [2]], [3, [1]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[1, 3, 0, 4, 2], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [4, 2, 3, 0, 1], [2, 0, 4, 1, 3]], [2], [[0, [4]], [1, [3]], [2, [2]], [3, [1]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225053,"parameters":{"n":5,"table":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0054","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 2, 4, 0, 3], [2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [0, 1, 2, 3, 4], [3, 0, 1, 4, 2]], [3], [[0, [4]], [1, [2]], [2, [1]], [3, [3]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[1, 2, 4, 0, 3], [2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [0, 1, 2, 3, 4], [3, 0, 1, 4, 2]], [3], [[0, [4]], [1, [2]], [2, [1]], [3, [3]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225054,"parameters":{"n":5,"table":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0055","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4]], [4], [[0, [3]], [1, [2]], [2, [1]], [3, [0]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4]], [4], [[0, [3]], [1, [2]], [2, [1]], [3, [0]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225055,"parameters":{"n":5,"table":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0056","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [4, 2, 0, 1, 3]], [0], [[0, [0]], [1, [3]], [2, [4]], [3, [1]], [4, [2]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [4, 2, 0, 1, 3]], [0], [[0, [0]], [1, [3]], [2, [4]], [3, [1]], [4, [2]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225056,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0057","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 0, 3, 1, 2], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3]], [1], [[0, [3]], [1, [1]], [2, [4]], [3, [0]], [4, [2]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 0, 3, 1, 2], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3]], [1], [[0, [3]], [1, [1]], [2, [4]], [3, [0]], [4, [2]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225057,"parameters":{"n":5,"table":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0058","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [2, 4, 3, 1, 0], [1, 2, 4, 0, 3]], [2], [[0, [3]], [1, [4]], [2, [2]], [3, [0]], [4, [1]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [2, 4, 3, 1, 0], [1, 2, 4, 0, 3]], [2], [[0, [3]], [1, [4]], [2, [2]], [3, [0]], [4, [1]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225058,"parameters":{"n":5,"table":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0059","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 2, 3, 0, 1], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [1, 3, 0, 4, 2]], [3], [[0, [2]], [1, [4]], [2, [0]], [3, [3]], [4, [1]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 2, 3, 0, 1], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [1, 3, 0, 4, 2]], [3], [[0, [2]], [1, [4]], [2, [0]], [3, [3]], [4, [1]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225059,"parameters":{"n":5,"table":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0060","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 2, 4, 1, 0], [2, 0, 3, 4, 1], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4]], [4], [[0, [2]], [1, [3]], [2, [0]], [3, [1]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 2, 4, 1, 0], [2, 0, 3, 4, 1], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4]], [4], [[0, [2]], [1, [3]], [2, [0]], [3, [1]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225060,"parameters":{"n":5,"table":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0061","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 4, 0, 2, 3], [2, 0, 3, 4, 1], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2]], [0], [[0, [0]], [1, [2]], [2, [1]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 4, 0, 2, 3], [2, 0, 3, 4, 1], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2]], [0], [[0, [0]], [1, [2]], [2, [1]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225061,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0062","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2]], [1], [[0, [2]], [1, [1]], [2, [0]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2]], [1], [[0, [2]], [1, [1]], [2, [0]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225062,"parameters":{"n":5,"table":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0063","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [3, 0, 4, 2, 1]], [2], [[0, [1]], [1, [0]], [2, [2]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [3, 0, 4, 2, 1]], [2], [[0, [1]], [1, [0]], [2, [2]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225063,"parameters":{"n":5,"table":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0064","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 3, 1, 0, 2], [3, 2, 4, 1, 0], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4], [2, 0, 3, 4, 1]], [3], [[0, [1]], [1, [0]], [2, [4]], [3, [3]], [4, [2]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 3, 1, 0, 2], [3, 2, 4, 1, 0], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4], [2, 0, 3, 4, 1]], [3], [[0, [1]], [1, [0]], [2, [4]], [3, [3]], [4, [2]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225064,"parameters":{"n":5,"table":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0065","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 4, 1, 2, 0], [4, 2, 3, 0, 1], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [0, 1, 2, 3, 4]], [4], [[0, [1]], [1, [0]], [2, [3]], [3, [2]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 4, 1, 2, 0], [4, 2, 3, 0, 1], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [0, 1, 2, 3, 4]], [4], [[0, [1]], [1, [0]], [2, [3]], [3, [2]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225065,"parameters":{"n":5,"table":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0066","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [4, 2, 3, 0, 1]], [0], [[0, [0]], [1, [2]], [2, [1]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [4, 2, 3, 0, 1]], [0], [[0, [0]], [1, [2]], [2, [1]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225066,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0067","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [1, 2, 4, 0, 3], [4, 3, 0, 2, 1], [2, 4, 3, 1, 0]], [1], [[0, [2]], [1, [1]], [2, [0]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [1, 2, 4, 0, 3], [4, 3, 0, 2, 1], [2, 4, 3, 1, 0]], [1], [[0, [2]], [1, [1]], [2, [0]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225067,"parameters":{"n":5,"table":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0068","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 2, 0, 4, 1], [2, 4, 1, 0, 3], [0, 1, 2, 3, 4], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0]], [2], [[0, [1]], [1, [0]], [2, [2]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 2, 0, 4, 1], [2, 4, 1, 0, 3], [0, 1, 2, 3, 4], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0]], [2], [[0, [1]], [1, [0]], [2, [2]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225068,"parameters":{"n":5,"table":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0069","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0]], [3], [[0, [1]], [1, [0]], [2, [4]], [3, [3]], [4, [2]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0]], [3], [[0, [1]], [1, [0]], [2, [4]], [3, [3]], [4, [2]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225069,"parameters":{"n":5,"table":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0070","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [1, 2, 4, 0, 3], [0, 1, 2, 3, 4]], [4], [[0, [1]], [1, [0]], [2, [3]], [3, [2]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [1, 2, 4, 0, 3], [0, 1, 2, 3, 4]], [4], [[0, [1]], [1, [0]], [2, [3]], [3, [2]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225070,"parameters":{"n":5,"table":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0071","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3], [3, 2, 0, 4, 1], [4, 0, 3, 1, 2]], [0], [[0, [0]], [1, [4]], [2, [3]], [3, [2]], [4, [1]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3], [3, 2, 0, 4, 1], [4, 0, 3, 1, 2]], [0], [[0, [0]], [1, [4]], [2, [3]], [3, [2]], [4, [1]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225071,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0072","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 0, 4, 2, 1], [0, 1, 2, 3, 4], [4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [1, 4, 3, 0, 2]], [1], [[0, [4]], [1, [1]], [2, [3]], [3, [2]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 0, 4, 2, 1], [0, 1, 2, 3, 4], [4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [1, 4, 3, 0, 2]], [1], [[0, [4]], [1, [1]], [2, [3]], [3, [2]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225072,"parameters":{"n":5,"table":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0073","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1]], [2], [[0, [4]], [1, [3]], [2, [2]], [3, [1]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1]], [2], [[0, [4]], [1, [3]], [2, [2]], [3, [1]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225073,"parameters":{"n":5,"table":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0074","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 4, 1, 0, 3], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1]], [3], [[0, [4]], [1, [2]], [2, [1]], [3, [3]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 4, 1, 0, 3], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1]], [3], [[0, [4]], [1, [2]], [2, [1]], [3, [3]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225074,"parameters":{"n":5,"table":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0075","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-identity-inverse-inventory；資料={\"n\":5,\"table\":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]]}。請依 [n,table,identities,inverse_rows,all_have_inverse] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [1, 4, 3, 0, 2], [4, 2, 0, 1, 3], [0, 1, 2, 3, 4]], [4], [[0, [3]], [1, [2]], [2, [1]], [3, [0]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [1, 4, 3, 0, 2], [4, 2, 0, 1, 3], [0, 1, 2, 3, 4]], [4], [[0, [3]], [1, [2]], [2, [1]], [3, [0]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-identity-inverse-inventory","seed":202610225075,"parameters":{"n":5,"table":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-identity-inverse-inventory","semantic_template":"qf-str22-group-identity-inverse-inventory/{\"n\":5,\"table\":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0076","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], 是, 是, [0], [[0, [0]], [1, [4]], [2, [3]], [3, [2]], [4, [1]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3]], 是, 是, [0], [[0, [0]], [1, [4]], [2, [3]], [3, [2]], [4, [1]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225076,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0077","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 0, 3, 4, 1], [0, 1, 2, 3, 4], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3]], 是, 是, [1], [[0, [4]], [1, [1]], [2, [3]], [3, [2]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 0, 3, 4, 1], [0, 1, 2, 3, 4], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3]], 是, 是, [1], [[0, [4]], [1, [1]], [2, [3]], [3, [2]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225077,"parameters":{"n":5,"table":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[2,0,3,4,1],[0,1,2,3,4],[3,2,4,1,0],[4,3,1,0,2],[1,4,0,2,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0078","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 3, 0, 4, 2], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [4, 2, 3, 0, 1], [2, 0, 4, 1, 3]], 是, 是, [2], [[0, [4]], [1, [3]], [2, [2]], [3, [1]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[1, 3, 0, 4, 2], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [4, 2, 3, 0, 1], [2, 0, 4, 1, 3]], 是, 是, [2], [[0, [4]], [1, [3]], [2, [2]], [3, [1]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225078,"parameters":{"n":5,"table":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[1,3,0,4,2],[3,4,1,2,0],[0,1,2,3,4],[4,2,3,0,1],[2,0,4,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0079","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 2, 4, 0, 3], [2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [0, 1, 2, 3, 4], [3, 0, 1, 4, 2]], 是, 是, [3], [[0, [4]], [1, [2]], [2, [1]], [3, [3]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[1, 2, 4, 0, 3], [2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [0, 1, 2, 3, 4], [3, 0, 1, 4, 2]], 是, 是, [3], [[0, [4]], [1, [2]], [2, [1]], [3, [3]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225079,"parameters":{"n":5,"table":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[1,2,4,0,3],[2,4,3,1,0],[4,3,0,2,1],[0,1,2,3,4],[3,0,1,4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0080","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [3]], [1, [2]], [2, [1]], [3, [0]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [3]], [1, [2]], [2, [1]], [3, [0]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225080,"parameters":{"n":5,"table":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0081","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [4, 2, 0, 1, 3]], 是, 是, [0], [[0, [0]], [1, [3]], [2, [4]], [3, [1]], [4, [2]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [4, 2, 0, 1, 3]], 是, 是, [0], [[0, [0]], [1, [3]], [2, [4]], [3, [1]], [4, [2]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225081,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,4,3,0,2],[2,3,1,4,0],[3,0,4,2,1],[4,2,0,1,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0082","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 0, 3, 1, 2], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3]], 是, 是, [1], [[0, [3]], [1, [1]], [2, [4]], [3, [0]], [4, [2]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 0, 3, 1, 2], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3]], 是, 是, [1], [[0, [3]], [1, [1]], [2, [4]], [3, [0]], [4, [2]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225082,"parameters":{"n":5,"table":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[4,0,3,1,2],[0,1,2,3,4],[3,2,0,4,1],[1,3,4,2,0],[2,4,1,0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0083","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [2, 4, 3, 1, 0], [1, 2, 4, 0, 3]], 是, 是, [2], [[0, [3]], [1, [4]], [2, [2]], [3, [0]], [4, [1]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [2, 4, 3, 1, 0], [1, 2, 4, 0, 3]], 是, 是, [2], [[0, [3]], [1, [4]], [2, [2]], [3, [0]], [4, [1]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225083,"parameters":{"n":5,"table":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[4,3,0,2,1],[3,0,1,4,2],[0,1,2,3,4],[2,4,3,1,0],[1,2,4,0,3]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0084","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 2, 3, 0, 1], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [1, 3, 0, 4, 2]], 是, 是, [3], [[0, [2]], [1, [4]], [2, [0]], [3, [3]], [4, [1]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 2, 3, 0, 1], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [0, 1, 2, 3, 4], [1, 3, 0, 4, 2]], 是, 是, [3], [[0, [2]], [1, [4]], [2, [0]], [3, [3]], [4, [1]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225084,"parameters":{"n":5,"table":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[4,2,3,0,1],[2,0,4,1,3],[3,4,1,2,0],[0,1,2,3,4],[1,3,0,4,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0085","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 2, 4, 1, 0], [2, 0, 3, 4, 1], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [2]], [1, [3]], [2, [0]], [3, [1]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 2, 4, 1, 0], [2, 0, 3, 4, 1], [4, 3, 1, 0, 2], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [2]], [1, [3]], [2, [0]], [3, [1]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225085,"parameters":{"n":5,"table":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[3,2,4,1,0],[2,0,3,4,1],[4,3,1,0,2],[1,4,0,2,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0086","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 4, 0, 2, 3], [2, 0, 3, 4, 1], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2]], 是, 是, [0], [[0, [0]], [1, [2]], [2, [1]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 4, 0, 2, 3], [2, 0, 3, 4, 1], [3, 2, 4, 1, 0], [4, 3, 1, 0, 2]], 是, 是, [0], [[0, [0]], [1, [2]], [2, [1]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225086,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,4,0,2,3],[2,0,3,4,1],[3,2,4,1,0],[4,3,1,0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0087","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2]], 是, 是, [1], [[0, [2]], [1, [1]], [2, [0]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1], [3, 4, 0, 1, 2]], 是, 是, [1], [[0, [2]], [1, [1]], [2, [0]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225087,"parameters":{"n":5,"table":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1],[3,4,0,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0088","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [3, 0, 4, 2, 1]], 是, 是, [2], [[0, [1]], [1, [0]], [2, [2]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [0, 1, 2, 3, 4], [1, 4, 3, 0, 2], [3, 0, 4, 2, 1]], 是, 是, [2], [[0, [1]], [1, [0]], [2, [2]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225088,"parameters":{"n":5,"table":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[4,2,0,1,3],[2,3,1,4,0],[0,1,2,3,4],[1,4,3,0,2],[3,0,4,2,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0089","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[4, 3, 1, 0, 2], [3, 2, 4, 1, 0], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4], [2, 0, 3, 4, 1]], 是, 是, [3], [[0, [1]], [1, [0]], [2, [4]], [3, [3]], [4, [2]]], 是)","explanation_zh":"結構基礎核對=(5, [[4, 3, 1, 0, 2], [3, 2, 4, 1, 0], [1, 4, 0, 2, 3], [0, 1, 2, 3, 4], [2, 0, 3, 4, 1]], 是, 是, [3], [[0, [1]], [1, [0]], [2, [4]], [3, [3]], [4, [2]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225089,"parameters":{"n":5,"table":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[4,3,1,0,2],[3,2,4,1,0],[1,4,0,2,3],[0,1,2,3,4],[2,0,3,4,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0090","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 4, 1, 2, 0], [4, 2, 3, 0, 1], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [1]], [1, [0]], [2, [3]], [3, [2]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 4, 1, 2, 0], [4, 2, 3, 0, 1], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [1]], [1, [0]], [2, [3]], [3, [2]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225090,"parameters":{"n":5,"table":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[3,4,1,2,0],[4,2,3,0,1],[1,3,0,4,2],[2,0,4,1,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0091","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [4, 2, 3, 0, 1]], 是, 是, [0], [[0, [0]], [1, [2]], [2, [1]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 3, 0, 4, 2], [2, 0, 4, 1, 3], [3, 4, 1, 2, 0], [4, 2, 3, 0, 1]], 是, 是, [0], [[0, [0]], [1, [2]], [2, [1]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225091,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,3,0,4,2],[2,0,4,1,3],[3,4,1,2,0],[4,2,3,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0092","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [1, 2, 4, 0, 3], [4, 3, 0, 2, 1], [2, 4, 3, 1, 0]], 是, 是, [1], [[0, [2]], [1, [1]], [2, [0]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 0, 1, 4, 2], [0, 1, 2, 3, 4], [1, 2, 4, 0, 3], [4, 3, 0, 2, 1], [2, 4, 3, 1, 0]], 是, 是, [1], [[0, [2]], [1, [1]], [2, [0]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225092,"parameters":{"n":5,"table":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[3,0,1,4,2],[0,1,2,3,4],[1,2,4,0,3],[4,3,0,2,1],[2,4,3,1,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0093","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 2, 0, 4, 1], [2, 4, 1, 0, 3], [0, 1, 2, 3, 4], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0]], 是, 是, [2], [[0, [1]], [1, [0]], [2, [2]], [3, [4]], [4, [3]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 2, 0, 4, 1], [2, 4, 1, 0, 3], [0, 1, 2, 3, 4], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0]], 是, 是, [2], [[0, [1]], [1, [0]], [2, [2]], [3, [4]], [4, [3]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225093,"parameters":{"n":5,"table":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[3,2,0,4,1],[2,4,1,0,3],[0,1,2,3,4],[4,0,3,1,2],[1,3,4,2,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0094","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0]], 是, 是, [3], [[0, [1]], [1, [0]], [2, [4]], [3, [3]], [4, [2]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 3, 4, 0, 1], [3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0]], 是, 是, [3], [[0, [1]], [1, [0]], [2, [4]], [3, [3]], [4, [2]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225094,"parameters":{"n":5,"table":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[2,3,4,0,1],[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0095","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [1, 2, 4, 0, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [1]], [1, [0]], [2, [3]], [3, [2]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 4, 3, 1, 0], [4, 3, 0, 2, 1], [3, 0, 1, 4, 2], [1, 2, 4, 0, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [1]], [1, [0]], [2, [3]], [3, [2]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225095,"parameters":{"n":5,"table":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[2,4,3,1,0],[4,3,0,2,1],[3,0,1,4,2],[1,2,4,0,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0096","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[0, 1, 2, 3, 4], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3], [3, 2, 0, 4, 1], [4, 0, 3, 1, 2]], 是, 是, [0], [[0, [0]], [1, [4]], [2, [3]], [3, [2]], [4, [1]]], 是)","explanation_zh":"結構基礎核對=(5, [[0, 1, 2, 3, 4], [1, 3, 4, 2, 0], [2, 4, 1, 0, 3], [3, 2, 0, 4, 1], [4, 0, 3, 1, 2]], 是, 是, [0], [[0, [0]], [1, [4]], [2, [3]], [3, [2]], [4, [1]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225096,"parameters":{"n":5,"table":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[0,1,2,3,4],[1,3,4,2,0],[2,4,1,0,3],[3,2,0,4,1],[4,0,3,1,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0097","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 0, 4, 2, 1], [0, 1, 2, 3, 4], [4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [1, 4, 3, 0, 2]], 是, 是, [1], [[0, [4]], [1, [1]], [2, [3]], [3, [2]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 0, 4, 2, 1], [0, 1, 2, 3, 4], [4, 2, 0, 1, 3], [2, 3, 1, 4, 0], [1, 4, 3, 0, 2]], 是, 是, [1], [[0, [4]], [1, [1]], [2, [3]], [3, [2]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225097,"parameters":{"n":5,"table":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[3,0,4,2,1],[0,1,2,3,4],[4,2,0,1,3],[2,3,1,4,0],[1,4,3,0,2]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0098","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1]], 是, 是, [2], [[0, [4]], [1, [3]], [2, [2]], [3, [1]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[3, 4, 0, 1, 2], [4, 0, 1, 2, 3], [0, 1, 2, 3, 4], [1, 2, 3, 4, 0], [2, 3, 4, 0, 1]], 是, 是, [2], [[0, [4]], [1, [3]], [2, [2]], [3, [1]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225098,"parameters":{"n":5,"table":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[3,4,0,1,2],[4,0,1,2,3],[0,1,2,3,4],[1,2,3,4,0],[2,3,4,0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0099","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 4, 1, 0, 3], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1]], 是, 是, [3], [[0, [4]], [1, [2]], [2, [1]], [3, [3]], [4, [0]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 4, 1, 0, 3], [4, 0, 3, 1, 2], [1, 3, 4, 2, 0], [0, 1, 2, 3, 4], [3, 2, 0, 4, 1]], 是, 是, [3], [[0, [4]], [1, [2]], [2, [1]], [3, [3]], [4, [0]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225099,"parameters":{"n":5,"table":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[2,4,1,0,3],[4,0,3,1,2],[1,3,4,2,0],[0,1,2,3,4],[3,2,0,4,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261022-r05-finite-group-0100","batch_id":"batch-20261013-advance-20261022-r05-finite-group-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-group"],"title_zh":"完整有限群表","stem_zh":"完整有限Cayley表。操作=group-full-group-audit；資料={\"n\":5,\"table\":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]]}。請依 [n,table,closed,associative,identities,inverse_rows,group] 欄序回答。","answer":{"kind":"expression","value":"(5, [[2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [1, 4, 3, 0, 2], [4, 2, 0, 1, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [3]], [1, [2]], [2, [1]], [3, [0]], [4, [4]]], 是)","explanation_zh":"結構基礎核對=(5, [[2, 3, 1, 4, 0], [3, 0, 4, 2, 1], [1, 4, 3, 0, 2], [4, 2, 0, 1, 3], [0, 1, 2, 3, 4]], 是, 是, [4], [[0, [3]], [1, [2]], [2, [1]], [3, [0]], [4, [4]]], 是)；依完整明示資料重算；完整明示的精確切片不是一般定理或經驗聲明；結合律逐三元組核對；抽樣不證群公理。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["完整有限群表"]},"variant":{"family_id":"qf-str22-group-full-group-audit","seed":202610225100,"parameters":{"n":5,"table":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]],"domain":"Complete_finite_operation_table","operation":"group-full-group-audit","semantic_template":"qf-str22-group-full-group-audit/{\"n\":5,\"table\":[[2,3,1,4,0],[3,0,4,2,1],[1,4,3,0,2],[4,2,0,1,3],[0,1,2,3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般定理、經驗預測、投資建議、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}