{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261101-r05-graph-matching-0001","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[2,3]],\"matching\":[0,1]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 1], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015001,"parameters":{"n":6,"edges":[[0,1],[2,3]],"matching":[0,1],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0002","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,2]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 2], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015002,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0003","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,2]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 2], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015003,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0004","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,3]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 3], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015004,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0005","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,2]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 2], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015005,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0006","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,3]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 3], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015006,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0007","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,3]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 3], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015007,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0008","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,4]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 4], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015008,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0009","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,2]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 2], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015009,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0010","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,3]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 3], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015010,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0011","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,3]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 3], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015011,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0012","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,4]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 4], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015012,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,3],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0013","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,3]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 3], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015013,"parameters":{"n":6,"edges":[[0,1],[1,2],[1,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0014","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,4]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 4], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015014,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0015","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,4]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 4], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015015,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0016","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,5]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 5], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 5], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015016,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],"matching":[0,5],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,5],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0017","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 1], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015017,"parameters":{"n":6,"edges":[[0,1],[2,3],[4,5]],"matching":[0,1],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0018","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,2]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 2], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015018,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0019","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,2]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 2], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015019,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0020","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,3]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 3], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015020,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3],[4,5]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0021","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,2]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 2], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015021,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0022","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,3]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 3], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015022,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3],[4,5]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0023","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,3]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 3], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 3], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015023,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3],[4,5]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0024","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,4]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 4], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015024,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0025","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-audit；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,2]}。請依 [matching_indexes,matching_edges,conflicting_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([0, 2], [[0, 1], [2, 3]], [], 是)","explanation_zh":"Wave5根節點核對=([0, 2], [[0, 1], [2, 3]], [], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-audit","seed":202611015025,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-audit","semantic_template":"qf-mod32-matching-audit/{\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0026","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[2,3]],\"matching\":[0,1]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015026,"parameters":{"n":6,"edges":[[0,1],[2,3]],"matching":[0,1],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0027","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,2]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015027,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0028","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,2]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015028,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0029","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,3]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015029,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0030","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,2]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015030,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0031","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,3]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015031,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0032","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,3]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015032,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0033","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,4]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015033,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0034","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,2]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015034,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0035","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,3]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015035,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0036","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,3]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015036,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0037","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,4]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015037,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,3],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0038","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,3]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015038,"parameters":{"n":6,"edges":[[0,1],[1,2],[1,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0039","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,4]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015039,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0040","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,4]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015040,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0041","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,5]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015041,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],"matching":[0,5],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,5],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0042","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0,1]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015042,"parameters":{"n":6,"edges":[[0,1],[2,3],[4,5]],"matching":[0,1],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0043","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,2]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015043,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0044","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,2]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015044,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0045","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,3]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015045,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3],[4,5]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0046","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,2]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015046,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0047","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,3]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015047,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3],[4,5]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0048","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,3]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015048,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3],[4,5]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0049","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,4]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015049,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0050","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-matched-vertices；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,2]}。請依 [matching_edges,matched_vertices,unmatched_vertices,valid_matching] 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)","explanation_zh":"Wave5根節點核對=([[0, 1], [2, 3]], [0, 1, 2, 3], [4, 5], 是)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-matched-vertices","seed":202611015050,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-matched-vertices","semantic_template":"qf-mod32-matching-matched-vertices/{\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0051","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[2,3]],\"matching\":[0,1]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015051,"parameters":{"n":6,"edges":[[0,1],[2,3]],"matching":[0,1],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0052","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,2]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015052,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0053","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,2]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015053,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0054","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,3]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015054,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0055","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,2]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015055,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0056","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,3]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015056,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0057","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,3]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015057,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0058","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,4]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015058,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0059","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,2]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015059,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0060","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,3]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015060,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0061","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,3]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015061,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0062","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,4]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015062,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,3],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0063","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,3]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015063,"parameters":{"n":6,"edges":[[0,1],[1,2],[1,3],[2,3]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0064","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,4]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015064,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0065","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,4]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015065,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0066","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,5]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [], 是, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015066,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],"matching":[0,5],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0,5],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0067","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0,1]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [2], 否, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [2], 否, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015067,"parameters":{"n":6,"edges":[[0,1],[2,3],[4,5]],"matching":[0,1],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0068","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,2]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [3], 否, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [3], 否, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015068,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0069","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,2]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [3], 否, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [3], 否, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015069,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0070","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,3]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [4], 否, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [4], 否, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015070,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3],[4,5]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0071","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,2]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [3], 否, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [3], 否, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015071,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0072","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,3]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [4], 否, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [4], 否, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015072,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3],[4,5]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0073","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,3]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [4], 否, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [4], 否, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015073,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3],[4,5]],"matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,3],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0074","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,4]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [5], 否, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [5], 否, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015074,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],"matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0,4],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0075","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximality-audit；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,2]}。請依 [valid_matching,addable_edge_indexes,maximal,boundary] 欄序回答。","answer":{"kind":"expression","value":"(是, [3], 否, maximal_not_necessarily_maximum)","explanation_zh":"Wave5根節點核對=(是, [3], 否, maximal_not_necessarily_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximality-audit","seed":202611015075,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3],[4,5]],"matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximality-audit","semantic_template":"qf-mod32-matching-maximality-audit/{\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0,2],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0076","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[2,3]],\"matching\":[0],\"larger_matching\":[0,1]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 1], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 1], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015076,"parameters":{"n":6,"edges":[[0,1],[2,3]],"matching":[0],"larger_matching":[0,1],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[2,3]],\"larger_matching\":[0,1],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0077","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3]],\"matching\":[0],\"larger_matching\":[0,2]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015077,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3]],"matching":[0],"larger_matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[2,3]],\"larger_matching\":[0,2],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0078","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3]],\"matching\":[0],\"larger_matching\":[0,2]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015078,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3]],"matching":[0],"larger_matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,3],[2,3]],\"larger_matching\":[0,2],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0079","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"matching\":[0],\"larger_matching\":[0,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015079,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3]],"matching":[0],"larger_matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[0,3],[2,3]],\"larger_matching\":[0,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0080","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3]],\"matching\":[0],\"larger_matching\":[0,2]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015080,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3]],"matching":[0],"larger_matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[1,2],[2,3]],\"larger_matching\":[0,2],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0081","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"matching\":[0],\"larger_matching\":[0,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015081,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3]],"matching":[0],"larger_matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[1,2],[2,3]],\"larger_matching\":[0,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0082","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"matching\":[0],\"larger_matching\":[0,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015082,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3]],"matching":[0],"larger_matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,3],[1,2],[2,3]],\"larger_matching\":[0,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0083","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"matching\":[0],\"larger_matching\":[0,4]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 4], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 4], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015083,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3]],"matching":[0],"larger_matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3]],\"larger_matching\":[0,4],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0084","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3]],\"matching\":[0],\"larger_matching\":[0,2]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015084,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3]],"matching":[0],"larger_matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[1,3],[2,3]],\"larger_matching\":[0,2],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0085","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"matching\":[0],\"larger_matching\":[1,2]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [1, 2], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [1, 2], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015085,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,3],[2,3]],"matching":[0],"larger_matching":[1,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[1,3],[2,3]],\"larger_matching\":[1,2],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0086","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"matching\":[0],\"larger_matching\":[0,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015086,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,3],[2,3]],"matching":[0],"larger_matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,3],[1,3],[2,3]],\"larger_matching\":[0,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0087","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"matching\":[0],\"larger_matching\":[1,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [1, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [1, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015087,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,3],[2,3]],"matching":[0],"larger_matching":[1,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[0,3],[1,3],[2,3]],\"larger_matching\":[1,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0088","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"matching\":[0],\"larger_matching\":[0,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015088,"parameters":{"n":6,"edges":[[0,1],[1,2],[1,3],[2,3]],"matching":[0],"larger_matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[1,2],[1,3],[2,3]],\"larger_matching\":[0,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0089","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"matching\":[0],\"larger_matching\":[1,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [1, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [1, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015089,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[1,3],[2,3]],"matching":[0],"larger_matching":[1,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[1,2],[1,3],[2,3]],\"larger_matching\":[1,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0090","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0],\"larger_matching\":[0,4]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 4], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 4], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015090,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[1,3],[2,3]],"matching":[0],"larger_matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,3],[1,2],[1,3],[2,3]],\"larger_matching\":[0,4],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0091","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"matching\":[0],\"larger_matching\":[1,4]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [1, 4], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [1, 4], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015091,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],"matching":[0],"larger_matching":[1,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[1,3],[2,3]],\"larger_matching\":[1,4],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0092","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,1]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 1], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 1], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015092,"parameters":{"n":6,"edges":[[0,1],[2,3],[4,5]],"matching":[0],"larger_matching":[0,1],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[2,3],[4,5]],\"larger_matching\":[0,1],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0093","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,2]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015093,"parameters":{"n":6,"edges":[[0,1],[0,2],[2,3],[4,5]],"matching":[0],"larger_matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[2,3],[4,5]],\"larger_matching\":[0,2],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0094","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,2]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015094,"parameters":{"n":6,"edges":[[0,1],[0,3],[2,3],[4,5]],"matching":[0],"larger_matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,3],[2,3],[4,5]],\"larger_matching\":[0,2],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0095","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015095,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[2,3],[4,5]],"matching":[0],"larger_matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[0,3],[2,3],[4,5]],\"larger_matching\":[0,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0096","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,2]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015096,"parameters":{"n":6,"edges":[[0,1],[1,2],[2,3],[4,5]],"matching":[0],"larger_matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[1,2],[2,3],[4,5]],\"larger_matching\":[0,2],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0097","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015097,"parameters":{"n":6,"edges":[[0,1],[0,2],[1,2],[2,3],[4,5]],"matching":[0],"larger_matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[1,2],[2,3],[4,5]],\"larger_matching\":[0,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0098","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,3]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 3], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015098,"parameters":{"n":6,"edges":[[0,1],[0,3],[1,2],[2,3],[4,5]],"matching":[0],"larger_matching":[0,3],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,3],[1,2],[2,3],[4,5]],\"larger_matching\":[0,3],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0099","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,4]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 4], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 4], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015099,"parameters":{"n":6,"edges":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],"matching":[0],"larger_matching":[0,4],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[0,2],[0,3],[1,2],[2,3],[4,5]],\"larger_matching\":[0,4],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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-20261101-r05-graph-matching-0100","batch_id":"batch-20261014-advance-20261101-r05-graph-matching-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-matching"],"title_zh":"圖匹配","stem_zh":"完整有限無向無loop簡單圖與原圖edge indexes。操作=matching-maximum-distinction；資料={\"n\":6,\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"matching\":[0],\"larger_matching\":[0,2]}。請依 [matching_indexes,larger_indexes,size,larger_size,witness,conclusion] 欄序回答。","answer":{"kind":"expression","value":"([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)","explanation_zh":"Wave5根節點核對=([0], [0, 2], 1, 2, 是, supplied_matching_not_maximum)；依完整明示資料重算；matching邊須兩兩端點不交且空matching合法；matching、maximal、maximum與perfect不可混同。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖匹配"]},"variant":{"family_id":"qf-mod32-matching-maximum-distinction","seed":202611015100,"parameters":{"n":6,"edges":[[0,1],[1,3],[2,3],[4,5]],"matching":[0],"larger_matching":[0,2],"domain":"Complete_finite_simple_graph_matching","operation":"matching-maximum-distinction","semantic_template":"qf-mod32-matching-maximum-distinction/{\"edges\":[[0,1],[1,3],[2,3],[4,5]],\"larger_matching\":[0,2],\"matching\":[0],\"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、一般compactness／a.s.定理／maximum matching／語言等價、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"}}