{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0001","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 2, [[0, 1]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(4, 2, [[0, 1]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036001,"parameters":{"n":6,"edges":[[0,1],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0002","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, [[0, 2]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(5, 2, [[0, 2]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036002,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0003","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, [[0, 2]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(5, 2, [[0, 2]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036003,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0004","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(6, 2, [[0, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(6, 2, [[0, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036004,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0005","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, [[0, 2]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(5, 2, [[0, 2]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036005,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[1,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0006","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(6, 2, [[0, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(6, 2, [[0, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036006,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0007","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(7, 2, [[1, 2], [0, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(7, 2, [[1, 2], [0, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036007,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0008","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, 2, [[2, 3], [0, 4]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(8, 2, [[2, 3], [0, 4]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036008,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0009","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, [[0, 2]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(5, 2, [[0, 2]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036009,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0010","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(7, 2, [[1, 2], [0, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(7, 2, [[1, 2], [0, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036010,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0011","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(6, 2, [[0, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(6, 2, [[0, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036011,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0012","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, 2, [[1, 3], [0, 4]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(8, 2, [[1, 3], [0, 4]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036012,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0013","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[1,2],[1,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(6, 2, [[0, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(6, 2, [[0, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036013,"parameters":{"n":6,"edges":[[0,1],[1,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0014","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, 2, [[1, 3], [0, 4]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(8, 2, [[1, 3], [0, 4]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036014,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0015","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, 2, [[1, 2], [0, 4]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(8, 2, [[1, 2], [0, 4]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036015,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0016","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, 2, [[2, 3], [1, 4], [0, 5]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(10, 2, [[2, 3], [1, 4], [0, 5]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036016,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0017","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, 3, [[0, 1, 2]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(8, 3, [[0, 1, 2]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036017,"parameters":{"n":6,"edges":[[0,1],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0018","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3],[4,5]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, 3, [[0, 2, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(10, 3, [[0, 2, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036018,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0019","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3],[4,5]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, 3, [[0, 2, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(10, 3, [[0, 2, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036019,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0020","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(12, 3, [[0, 3, 4]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(12, 3, [[0, 3, 4]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036020,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0021","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3],[4,5]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, 3, [[0, 2, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(10, 3, [[0, 2, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036021,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0022","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(12, 3, [[0, 3, 4]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(12, 3, [[0, 3, 4]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036022,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0023","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(14, 3, [[1, 2, 4], [0, 3, 4]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(14, 3, [[1, 2, 4], [0, 3, 4]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036023,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0024","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(16, 3, [[2, 3, 5], [0, 4, 5]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(16, 3, [[2, 3, 5], [0, 4, 5]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036024,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0025","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-size；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3],[4,5]]}。請依 [matching_count,maximum_size,maximum_matchings,certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, 3, [[0, 2, 3]], exhaustive_all_edge_subsets)","explanation_zh":"Wave5第三層核對=(10, 3, [[0, 2, 3]], exhaustive_all_edge_subsets)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-size","seed":202611036025,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-size","semantic_template":"qf-mod34-maxmatching-maximum-size/{\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0026","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 是, 2, 2, 是, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 是, 2, 2, 是, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036026,"parameters":{"n":6,"edges":[[0,1],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0027","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036027,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0028","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036028,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0029","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036029,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0030","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036030,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0031","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036031,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0032","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036032,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0033","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036033,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0034","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036034,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0035","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036035,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0036","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036036,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0037","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036037,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0038","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036038,"parameters":{"n":6,"edges":[[0,1],[1,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0039","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036039,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0040","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036040,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0041","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 2, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036041,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0042","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 是, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 是, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036042,"parameters":{"n":6,"edges":[[0,1],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0043","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036043,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0044","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036044,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0045","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036045,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0046","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036046,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0047","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036047,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0048","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036048,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0049","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036049,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0050","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximum-audit；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,size,maximum_size,is_maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)","explanation_zh":"Wave5第三層核對=([0, 1], 否, 2, 3, 否, maximum_not_necessarily_unique_or_perfect)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximum-audit","seed":202611036050,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximum-audit","semantic_template":"qf-mod34-maxmatching-maximum-audit/{\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0051","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 1]], 1, 否)","explanation_zh":"Wave5第三層核對=(2, [[0, 1]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036051,"parameters":{"n":6,"edges":[[0,1],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0052","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 2]], 1, 否)","explanation_zh":"Wave5第三層核對=(2, [[0, 2]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036052,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0053","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 2]], 1, 否)","explanation_zh":"Wave5第三層核對=(2, [[0, 2]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036053,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0054","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 3]], 1, 否)","explanation_zh":"Wave5第三層核對=(2, [[0, 3]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036054,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0055","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 2]], 1, 否)","explanation_zh":"Wave5第三層核對=(2, [[0, 2]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036055,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[1,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0056","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 3]], 1, 否)","explanation_zh":"Wave5第三層核對=(2, [[0, 3]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036056,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0057","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[1, 2], [0, 3]], 2, 是)","explanation_zh":"Wave5第三層核對=(2, [[1, 2], [0, 3]], 2, 是)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036057,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0058","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[2, 3], [0, 4]], 2, 是)","explanation_zh":"Wave5第三層核對=(2, [[2, 3], [0, 4]], 2, 是)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036058,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0059","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 2]], 1, 否)","explanation_zh":"Wave5第三層核對=(2, [[0, 2]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036059,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0060","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[1, 2], [0, 3]], 2, 是)","explanation_zh":"Wave5第三層核對=(2, [[1, 2], [0, 3]], 2, 是)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036060,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0061","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 3]], 1, 否)","explanation_zh":"Wave5第三層核對=(2, [[0, 3]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036061,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0062","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[1, 3], [0, 4]], 2, 是)","explanation_zh":"Wave5第三層核對=(2, [[1, 3], [0, 4]], 2, 是)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036062,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0063","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[1,2],[1,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[0, 3]], 1, 否)","explanation_zh":"Wave5第三層核對=(2, [[0, 3]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036063,"parameters":{"n":6,"edges":[[0,1],[1,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0064","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[1, 3], [0, 4]], 2, 是)","explanation_zh":"Wave5第三層核對=(2, [[1, 3], [0, 4]], 2, 是)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036064,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0065","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[1, 2], [0, 4]], 2, 是)","explanation_zh":"Wave5第三層核對=(2, [[1, 2], [0, 4]], 2, 是)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036065,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0066","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(2, [[2, 3], [1, 4], [0, 5]], 3, 是)","explanation_zh":"Wave5第三層核對=(2, [[2, 3], [1, 4], [0, 5]], 3, 是)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036066,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0067","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(3, [[0, 1, 2]], 1, 否)","explanation_zh":"Wave5第三層核對=(3, [[0, 1, 2]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036067,"parameters":{"n":6,"edges":[[0,1],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0068","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3],[4,5]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(3, [[0, 2, 3]], 1, 否)","explanation_zh":"Wave5第三層核對=(3, [[0, 2, 3]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036068,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0069","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3],[4,5]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(3, [[0, 2, 3]], 1, 否)","explanation_zh":"Wave5第三層核對=(3, [[0, 2, 3]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036069,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0070","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(3, [[0, 3, 4]], 1, 否)","explanation_zh":"Wave5第三層核對=(3, [[0, 3, 4]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036070,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0071","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3],[4,5]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(3, [[0, 2, 3]], 1, 否)","explanation_zh":"Wave5第三層核對=(3, [[0, 2, 3]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036071,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0072","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(3, [[0, 3, 4]], 1, 否)","explanation_zh":"Wave5第三層核對=(3, [[0, 3, 4]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036072,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0073","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(3, [[1, 2, 4], [0, 3, 4]], 2, 是)","explanation_zh":"Wave5第三層核對=(3, [[1, 2, 4], [0, 3, 4]], 2, 是)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036073,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0074","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(3, [[2, 3, 5], [0, 4, 5]], 2, 是)","explanation_zh":"Wave5第三層核對=(3, [[2, 3, 5], [0, 4, 5]], 2, 是)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036074,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0075","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-multiple-maxima；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3],[4,5]]}。請依 [maximum_size,maximum_matchings,count,multiple] 欄序回答。","answer":{"kind":"expression","value":"(3, [[0, 2, 3]], 1, 否)","explanation_zh":"Wave5第三層核對=(3, [[0, 2, 3]], 1, 否)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-multiple-maxima","seed":202611036075,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3],[4,5]],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-multiple-maxima","semantic_template":"qf-mod34-maxmatching-multiple-maxima/{\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0076","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 是, [], 是, 2, 是, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 是, [], 是, 2, 是, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036076,"parameters":{"n":6,"edges":[[0,1],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0077","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036077,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0078","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036078,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0079","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036079,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0080","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036080,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0081","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036081,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0082","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036082,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0083","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036083,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0084","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036084,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0085","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036085,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0086","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036086,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0087","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036087,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0088","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036088,"parameters":{"n":6,"edges":[[0,1],[1,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0089","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036089,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0090","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036090,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0091","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [], 否, 2, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036091,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0092","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 是, [2], 否, 3, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 是, [2], 否, 3, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036092,"parameters":{"n":6,"edges":[[0,1],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0093","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [3], 否, 3, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [3], 否, 3, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036093,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0094","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [3], 否, 3, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [3], 否, 3, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036094,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0095","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [4], 否, 3, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [4], 否, 3, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036095,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0096","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [3], 否, 3, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [3], 否, 3, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036096,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0097","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [4], 否, 3, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [4], 否, 3, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036097,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0098","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [4], 否, 3, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [4], 否, 3, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036098,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0099","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [5], 否, 3, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [5], 否, 3, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036099,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261103-r06-maximum-matching-0100","batch_id":"batch-20261014-advance-20261103-r06-maximum-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-maximum-matching"],"title_zh":"最大匹配","stem_zh":"edge count有界的完整有限簡單圖與全edge-subset枚舉。操作=maxmatching-maximal-vs-maximum；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching,valid,addable_edges,maximal,maximum_size,maximum,boundary] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], 否, [3], 否, 3, 否, maximal_and_maximum_are_distinct_properties)","explanation_zh":"Wave5第三層核對=([0, 1], 否, [3], 否, 3, 否, maximal_and_maximum_are_distinct_properties)；依完整明示資料重算；每個候選先核matching，maximum需全域比較；maximum不等於maximal、perfect或unique。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["最大匹配"]},"variant":{"family_id":"qf-mod34-maxmatching-maximal-vs-maximum","seed":202611036100,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3],[4,5]],"matching":[0,1],"domain":"Exhaustive_finite_graph_maximum_matching","operation":"maxmatching-maximal-vs-maximum","semantic_template":"qf-mod34-maxmatching-maximal-vs-maximum/{\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,1],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、sampled rank upper bound、infinite-domain uniformity、finite-prefix series proof、posterior/identifiability、graph connectivity、nonexhaustive maximum、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}