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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0021","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-bijection-audit；資料={\"n\":6,\"mapping\":[0,1,5,3,2,0]}。請依 [n,mapping,bijective] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 3, 2, 0], 否)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 3, 2, 0], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-bijection-audit","seed":202610266021,"parameters":{"n":6,"mapping":[0,1,5,3,2,0],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-bijection-audit","semantic_template":"qf-mod26-graphiso-bijection-audit/{\"mapping\":[0,1,5,3,2,0],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0022","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-bijection-audit；資料={\"n\":6,\"mapping\":[0,1,5,3,4,2]}。請依 [n,mapping,bijective] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 3, 4, 2], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 3, 4, 2], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-bijection-audit","seed":202610266022,"parameters":{"n":6,"mapping":[0,1,5,3,4,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-bijection-audit","semantic_template":"qf-mod26-graphiso-bijection-audit/{\"mapping\":[0,1,5,3,4,2],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0023","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-bijection-audit；資料={\"n\":6,\"mapping\":[0,1,5,4,2,3]}。請依 [n,mapping,bijective] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 4, 2, 3], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 4, 2, 3], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-bijection-audit","seed":202610266023,"parameters":{"n":6,"mapping":[0,1,5,4,2,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-bijection-audit","semantic_template":"qf-mod26-graphiso-bijection-audit/{\"mapping\":[0,1,5,4,2,3],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0024","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-bijection-audit；資料={\"n\":6,\"mapping\":[0,1,5,4,3,2]}。請依 [n,mapping,bijective] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 4, 3, 2], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 4, 3, 2], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-bijection-audit","seed":202610266024,"parameters":{"n":6,"mapping":[0,1,5,4,3,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-bijection-audit","semantic_template":"qf-mod26-graphiso-bijection-audit/{\"mapping\":[0,1,5,4,3,2],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0025","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-bijection-audit；資料={\"n\":6,\"mapping\":[0,2,1,3,4,5]}。請依 [n,mapping,bijective] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 1, 3, 4, 5], 是)","explanation_zh":"結構深度核對=(6, [0, 2, 1, 3, 4, 5], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-bijection-audit","seed":202610266025,"parameters":{"n":6,"mapping":[0,2,1,3,4,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-bijection-audit","semantic_template":"qf-mod26-graphiso-bijection-audit/{\"mapping\":[0,2,1,3,4,5],\"n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0026","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5],[0,2]],\"mapping\":[0,1,2,3,4,5]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [[0, 2, 否, 是]], 否)","explanation_zh":"結構深度核對=([0, 1, 2, 3, 4, 5], [[0, 2, 否, 是]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266026,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[0,2]],"mapping":[0,1,2,3,4,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,3,4,5],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,2],[2,3],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0027","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,3],[3,5],[4,5]],\"mapping\":[0,1,2,3,5,4]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5, 4], [], 是)","explanation_zh":"結構深度核對=([0, 1, 2, 3, 5, 4], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266027,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,3],[3,5],[4,5]],"mapping":[0,1,2,3,5,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,3,5,4],\"n\":6,\"right_edges\":[[0,1],[1,2],[2,3],[3,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0028","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,4],[3,4],[3,5]],\"mapping\":[0,1,2,4,3,5]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 4, 3, 5], [], 是)","explanation_zh":"結構深度核對=([0, 1, 2, 4, 3, 5], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266028,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,4],[3,4],[3,5]],"mapping":[0,1,2,4,3,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,4,3,5],\"n\":6,\"right_edges\":[[0,1],[1,2],[2,4],[3,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0029","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,4],[4,5],[3,5]],\"mapping\":[0,1,2,4,5,3]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 4, 5, 3], [], 是)","explanation_zh":"結構深度核對=([0, 1, 2, 4, 5, 3], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266029,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,4],[4,5],[3,5]],"mapping":[0,1,2,4,5,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,4,5,3],\"n\":6,\"right_edges\":[[0,1],[1,2],[2,4],[3,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0030","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,5],[3,5],[3,4]],\"mapping\":[0,1,2,5,3,4]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5, 3, 4], [], 是)","explanation_zh":"結構深度核對=([0, 1, 2, 5, 3, 4], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266030,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,5],[3,5],[3,4]],"mapping":[0,1,2,5,3,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,5,3,4],\"n\":6,\"right_edges\":[[0,1],[1,2],[2,5],[3,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0031","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,5],[4,5],[3,4],[0,2]],\"mapping\":[0,1,2,5,4,3]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5, 4, 3], [[0, 2, 否, 是]], 否)","explanation_zh":"結構深度核對=([0, 1, 2, 5, 4, 3], [[0, 2, 否, 是]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266031,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,5],[4,5],[3,4],[0,2]],"mapping":[0,1,2,5,4,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,5,4,3],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0032","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[2,3],[2,4],[4,5]],\"mapping\":[0,1,3,2,4,5]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 2, 4, 5], [], 是)","explanation_zh":"結構深度核對=([0, 1, 3, 2, 4, 5], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266032,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[2,3],[2,4],[4,5]],"mapping":[0,1,3,2,4,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,2,4,5],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,3],[2,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0033","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[2,3],[2,5],[4,5]],\"mapping\":[0,1,3,2,5,4]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 2, 5, 4], [], 是)","explanation_zh":"結構深度核對=([0, 1, 3, 2, 5, 4], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266033,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[2,3],[2,5],[4,5]],"mapping":[0,1,3,2,5,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,2,5,4],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,3],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0034","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[3,4],[2,4],[2,5]],\"mapping\":[0,1,3,4,2,5]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 4, 2, 5], [], 是)","explanation_zh":"結構深度核對=([0, 1, 3, 4, 2, 5], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266034,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[3,4],[2,4],[2,5]],"mapping":[0,1,3,4,2,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,4,2,5],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,4],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0035","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[3,4],[4,5],[2,5]],\"mapping\":[0,1,3,4,5,2]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 4, 5, 2], [], 是)","explanation_zh":"結構深度核對=([0, 1, 3, 4, 5, 2], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266035,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[3,4],[4,5],[2,5]],"mapping":[0,1,3,4,5,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,4,5,2],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0036","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[3,5],[2,5],[2,4],[0,2]],\"mapping\":[0,1,3,5,2,4]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 5, 2, 4], [[0, 4, 否, 是]], 否)","explanation_zh":"結構深度核對=([0, 1, 3, 5, 2, 4], [[0, 4, 否, 是]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266036,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[3,5],[2,5],[2,4],[0,2]],"mapping":[0,1,3,5,2,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,5,2,4],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,3],[2,4],[2,5],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0037","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[3,5],[4,5],[2,4]],\"mapping\":[0,1,3,5,4,2]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 3, 5, 4, 2], [], 是)","explanation_zh":"結構深度核對=([0, 1, 3, 5, 4, 2], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266037,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[3,5],[4,5],[2,4]],"mapping":[0,1,3,5,4,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,5,4,2],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,4],[3,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0038","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[2,4],[2,3],[3,5]],\"mapping\":[0,1,4,2,3,5]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 4, 2, 3, 5], [], 是)","explanation_zh":"結構深度核對=([0, 1, 4, 2, 3, 5], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266038,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[2,4],[2,3],[3,5]],"mapping":[0,1,4,2,3,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,2,3,5],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,3],[2,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0039","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[2,4],[2,5],[3,5]],\"mapping\":[0,1,4,2,5,3]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 4, 2, 5, 3], [], 是)","explanation_zh":"結構深度核對=([0, 1, 4, 2, 5, 3], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266039,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[2,4],[2,5],[3,5]],"mapping":[0,1,4,2,5,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,2,5,3],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,4],[2,5],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0040","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[3,4],[2,3],[2,5]],\"mapping\":[0,1,4,3,2,5]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 4, 3, 2, 5], [], 是)","explanation_zh":"結構深度核對=([0, 1, 4, 3, 2, 5], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266040,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[3,4],[2,3],[2,5]],"mapping":[0,1,4,3,2,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,3,2,5],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,3],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0041","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[3,4],[3,5],[2,5],[0,2]],\"mapping\":[0,1,4,3,5,2]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 4, 3, 5, 2], [[0, 5, 否, 是]], 否)","explanation_zh":"結構深度核對=([0, 1, 4, 3, 5, 2], [[0, 5, 否, 是]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266041,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[3,4],[3,5],[2,5],[0,2]],"mapping":[0,1,4,3,5,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,3,5,2],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,4],[2,5],[3,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0042","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[4,5],[2,5],[2,3]],\"mapping\":[0,1,4,5,2,3]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 4, 5, 2, 3], [], 是)","explanation_zh":"結構深度核對=([0, 1, 4, 5, 2, 3], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266042,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[4,5],[2,5],[2,3]],"mapping":[0,1,4,5,2,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,5,2,3],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,3],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0043","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[4,5],[3,5],[2,3]],\"mapping\":[0,1,4,5,3,2]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 4, 5, 3, 2], [], 是)","explanation_zh":"結構深度核對=([0, 1, 4, 5, 3, 2], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266043,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[4,5],[3,5],[2,3]],"mapping":[0,1,4,5,3,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,5,3,2],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,3],[3,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0044","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[2,5],[2,3],[3,4]],\"mapping\":[0,1,5,2,3,4]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 5, 2, 3, 4], [], 是)","explanation_zh":"結構深度核對=([0, 1, 5, 2, 3, 4], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266044,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[2,5],[2,3],[3,4]],"mapping":[0,1,5,2,3,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,2,3,4],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,3],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0045","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[2,5],[2,4],[3,4]],\"mapping\":[0,1,5,2,4,3]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 5, 2, 4, 3], [], 是)","explanation_zh":"結構深度核對=([0, 1, 5, 2, 4, 3], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266045,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[2,5],[2,4],[3,4]],"mapping":[0,1,5,2,4,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,2,4,3],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,4],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0046","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[3,5],[2,3],[2,4],[0,2]],\"mapping\":[0,1,5,3,2,4]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 5, 3, 2, 4], [[0, 4, 否, 是]], 否)","explanation_zh":"結構深度核對=([0, 1, 5, 3, 2, 4], [[0, 4, 否, 是]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266046,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[3,5],[2,3],[2,4],[0,2]],"mapping":[0,1,5,3,2,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,3,2,4],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,5],[2,3],[2,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0047","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[3,5],[3,4],[2,4]],\"mapping\":[0,1,5,3,4,2]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 5, 3, 4, 2], [], 是)","explanation_zh":"結構深度核對=([0, 1, 5, 3, 4, 2], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266047,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[3,5],[3,4],[2,4]],"mapping":[0,1,5,3,4,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,3,4,2],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,4],[3,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0048","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[4,5],[2,4],[2,3]],\"mapping\":[0,1,5,4,2,3]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 5, 4, 2, 3], [], 是)","explanation_zh":"結構深度核對=([0, 1, 5, 4, 2, 3], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266048,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[4,5],[2,4],[2,3]],"mapping":[0,1,5,4,2,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,4,2,3],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,3],[2,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0049","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[4,5],[3,4],[2,3]],\"mapping\":[0,1,5,4,3,2]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 5, 4, 3, 2], [], 是)","explanation_zh":"結構深度核對=([0, 1, 5, 4, 3, 2], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266049,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[4,5],[3,4],[2,3]],"mapping":[0,1,5,4,3,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,4,3,2],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,3],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0050","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-adjacency-iff-audit；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,2],[1,2],[1,3],[3,4],[4,5]],\"mapping\":[0,2,1,3,4,5]}。請依 [mapping,bad_pairs,adjacency_iff] 欄序回答。","answer":{"kind":"expression","value":"([0, 2, 1, 3, 4, 5], [], 是)","explanation_zh":"結構深度核對=([0, 2, 1, 3, 4, 5], [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-adjacency-iff-audit","seed":202610266050,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,2],[1,2],[1,3],[3,4],[4,5]],"mapping":[0,2,1,3,4,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-adjacency-iff-audit","semantic_template":"qf-mod26-graphiso-adjacency-iff-audit/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,2,1,3,4,5],\"n\":6,\"right_edges\":[[0,2],[1,2],[1,3],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0051","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5],[0,2]],\"mapping\":[0,1,2,3,4,0]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 3, 4, 0], 否, [[0, 2, 否, 是], [1, 5, 否, 是], [2, 5, 否, 是], [4, 5, 是, 否]], 否)","explanation_zh":"結構深度核對=(6, [0, 1, 2, 3, 4, 0], 否, [[0, 2, 否, 是], [1, 5, 否, 是], [2, 5, 否, 是], [4, 5, 是, 否]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266051,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,3],[3,4],[4,5],[0,2]],"mapping":[0,1,2,3,4,0],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,3,4,0],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,2],[2,3],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0052","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,3],[3,5],[4,5]],\"mapping\":[0,1,2,3,5,4]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 3, 5, 4], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 2, 3, 5, 4], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266052,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,3],[3,5],[4,5]],"mapping":[0,1,2,3,5,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,3,5,4],\"n\":6,\"right_edges\":[[0,1],[1,2],[2,3],[3,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0053","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,4],[3,4],[3,5]],\"mapping\":[0,1,2,4,3,5]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 4, 3, 5], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 2, 4, 3, 5], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266053,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,4],[3,4],[3,5]],"mapping":[0,1,2,4,3,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,4,3,5],\"n\":6,\"right_edges\":[[0,1],[1,2],[2,4],[3,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0054","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,4],[4,5],[3,5]],\"mapping\":[0,1,2,4,5,3]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 4, 5, 3], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 2, 4, 5, 3], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266054,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,4],[4,5],[3,5]],"mapping":[0,1,2,4,5,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,4,5,3],\"n\":6,\"right_edges\":[[0,1],[1,2],[2,4],[3,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0055","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,5],[3,5],[3,4]],\"mapping\":[0,1,2,5,3,4]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 5, 3, 4], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 2, 5, 3, 4], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266055,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,5],[3,5],[3,4]],"mapping":[0,1,2,5,3,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,5,3,4],\"n\":6,\"right_edges\":[[0,1],[1,2],[2,5],[3,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0056","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,2],[2,5],[4,5],[3,4],[0,2]],\"mapping\":[0,1,2,5,4,3]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 5, 4, 3], 是, [[0, 2, 否, 是]], 否)","explanation_zh":"結構深度核對=(6, [0, 1, 2, 5, 4, 3], 是, [[0, 2, 否, 是]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266056,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,2],[2,5],[4,5],[3,4],[0,2]],"mapping":[0,1,2,5,4,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,2,5,4,3],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0057","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[2,3],[2,4],[4,5]],\"mapping\":[0,1,3,2,4,5]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3, 2, 4, 5], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 3, 2, 4, 5], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266057,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[2,3],[2,4],[4,5]],"mapping":[0,1,3,2,4,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,2,4,5],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,3],[2,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0058","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[2,3],[2,5],[4,5]],\"mapping\":[0,1,3,2,5,0]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3, 2, 5, 0], 否, [[1, 5, 否, 是], [4, 5, 是, 否]], 否)","explanation_zh":"結構深度核對=(6, [0, 1, 3, 2, 5, 0], 否, [[1, 5, 否, 是], [4, 5, 是, 否]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266058,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[2,3],[2,5],[4,5]],"mapping":[0,1,3,2,5,0],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,2,5,0],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,3],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0059","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[3,4],[2,4],[2,5]],\"mapping\":[0,1,3,4,2,5]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3, 4, 2, 5], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 3, 4, 2, 5], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266059,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[3,4],[2,4],[2,5]],"mapping":[0,1,3,4,2,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,4,2,5],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,4],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0060","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[3,4],[4,5],[2,5]],\"mapping\":[0,1,3,4,5,2]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3, 4, 5, 2], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 3, 4, 5, 2], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266060,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[3,4],[4,5],[2,5]],"mapping":[0,1,3,4,5,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,4,5,2],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0061","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[3,5],[2,5],[2,4],[0,2]],\"mapping\":[0,1,3,5,2,4]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3, 5, 2, 4], 是, [[0, 4, 否, 是]], 否)","explanation_zh":"結構深度核對=(6, [0, 1, 3, 5, 2, 4], 是, [[0, 4, 否, 是]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266061,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[3,5],[2,5],[2,4],[0,2]],"mapping":[0,1,3,5,2,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,5,2,4],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,3],[2,4],[2,5],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0062","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,3],[3,5],[4,5],[2,4]],\"mapping\":[0,1,3,5,4,2]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3, 5, 4, 2], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 3, 5, 4, 2], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266062,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,3],[3,5],[4,5],[2,4]],"mapping":[0,1,3,5,4,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,3,5,4,2],\"n\":6,\"right_edges\":[[0,1],[1,3],[2,4],[3,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0063","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[2,4],[2,3],[3,5]],\"mapping\":[0,1,4,2,3,5]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 4, 2, 3, 5], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 4, 2, 3, 5], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266063,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[2,4],[2,3],[3,5]],"mapping":[0,1,4,2,3,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,2,3,5],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,3],[2,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0064","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[2,4],[2,5],[3,5]],\"mapping\":[0,1,4,2,5,3]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 4, 2, 5, 3], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 4, 2, 5, 3], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266064,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[2,4],[2,5],[3,5]],"mapping":[0,1,4,2,5,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,2,5,3],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,4],[2,5],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0065","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[3,4],[2,3],[2,5]],\"mapping\":[0,1,4,3,2,0]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 4, 3, 2, 0], 否, [[1, 5, 否, 是], [4, 5, 是, 否]], 否)","explanation_zh":"結構深度核對=(6, [0, 1, 4, 3, 2, 0], 否, [[1, 5, 否, 是], [4, 5, 是, 否]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266065,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[3,4],[2,3],[2,5]],"mapping":[0,1,4,3,2,0],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,3,2,0],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,3],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0066","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[3,4],[3,5],[2,5],[0,2]],\"mapping\":[0,1,4,3,5,2]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 4, 3, 5, 2], 是, [[0, 5, 否, 是]], 否)","explanation_zh":"結構深度核對=(6, [0, 1, 4, 3, 5, 2], 是, [[0, 5, 否, 是]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266066,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[3,4],[3,5],[2,5],[0,2]],"mapping":[0,1,4,3,5,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,3,5,2],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,4],[2,5],[3,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0067","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[4,5],[2,5],[2,3]],\"mapping\":[0,1,4,5,2,3]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 4, 5, 2, 3], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 4, 5, 2, 3], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266067,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[4,5],[2,5],[2,3]],"mapping":[0,1,4,5,2,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,5,2,3],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,3],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0068","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,4],[4,5],[3,5],[2,3]],\"mapping\":[0,1,4,5,3,2]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 4, 5, 3, 2], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 4, 5, 3, 2], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266068,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,4],[4,5],[3,5],[2,3]],"mapping":[0,1,4,5,3,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,4,5,3,2],\"n\":6,\"right_edges\":[[0,1],[1,4],[2,3],[3,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0069","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[2,5],[2,3],[3,4]],\"mapping\":[0,1,5,2,3,4]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 2, 3, 4], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 2, 3, 4], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266069,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[2,5],[2,3],[3,4]],"mapping":[0,1,5,2,3,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,2,3,4],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,3],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0070","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[2,5],[2,4],[3,4]],\"mapping\":[0,1,5,2,4,3]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 2, 4, 3], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 2, 4, 3], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266070,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[2,5],[2,4],[3,4]],"mapping":[0,1,5,2,4,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,2,4,3],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,4],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0071","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[3,5],[2,3],[2,4],[0,2]],\"mapping\":[0,1,5,3,2,4]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 3, 2, 4], 是, [[0, 4, 否, 是]], 否)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 3, 2, 4], 是, [[0, 4, 否, 是]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266071,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[3,5],[2,3],[2,4],[0,2]],"mapping":[0,1,5,3,2,4],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,3,2,4],\"n\":6,\"right_edges\":[[0,1],[0,2],[1,5],[2,3],[2,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0072","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[3,5],[3,4],[2,4]],\"mapping\":[0,1,5,3,4,0]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 3, 4, 0], 否, [[1, 5, 否, 是], [4, 5, 是, 否]], 否)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 3, 4, 0], 否, [[1, 5, 否, 是], [4, 5, 是, 否]], 否)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266072,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[3,5],[3,4],[2,4]],"mapping":[0,1,5,3,4,0],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,3,4,0],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,4],[3,4],[3,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0073","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[4,5],[2,4],[2,3]],\"mapping\":[0,1,5,4,2,3]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 4, 2, 3], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 4, 2, 3], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266073,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[4,5],[2,4],[2,3]],"mapping":[0,1,5,4,2,3],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,4,2,3],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,3],[2,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0074","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,1],[1,5],[4,5],[3,4],[2,3]],\"mapping\":[0,1,5,4,3,2]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 5, 4, 3, 2], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 1, 5, 4, 3, 2], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266074,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,1],[1,5],[4,5],[3,4],[2,3]],"mapping":[0,1,5,4,3,2],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,1,5,4,3,2],\"n\":6,\"right_edges\":[[0,1],[1,5],[2,3],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0075","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-qualification；資料={\"n\":6,\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"right_edges\":[[0,2],[1,2],[1,3],[3,4],[4,5]],\"mapping\":[0,2,1,3,4,5]}。請依 [n,mapping,bijective,bad_pairs,isomorphism] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 1, 3, 4, 5], 是, [], 是)","explanation_zh":"結構深度核對=(6, [0, 2, 1, 3, 4, 5], 是, [], 是)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-qualification","seed":202610266075,"parameters":{"n":6,"left_edges":[[0,1],[1,2],[2,3],[3,4],[4,5]],"right_edges":[[0,2],[1,2],[1,3],[3,4],[4,5]],"mapping":[0,2,1,3,4,5],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-qualification","semantic_template":"qf-mod26-graphiso-qualification/{\"left_edges\":[[0,1],[1,2],[2,3],[3,4],[4,5]],\"mapping\":[0,2,1,3,4,5],\"n\":6,\"right_edges\":[[0,2],[1,2],[1,3],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0076","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1]],\"right_n\":6,\"right_edges\":[[0,1],[0,3],[1,2]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 0, 1, 1], 6, [0, 0, 1, 1, 2, 2], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 0, 1, 1], 6, [0, 0, 1, 1, 2, 2], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266076,"parameters":{"left_n":6,"left_edges":[[0,1]],"right_n":6,"right_edges":[[0,1],[0,3],[1,2]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1]],\"left_n\":6,\"right_edges\":[[0,1],[0,3],[1,2]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0077","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,2]],\"right_n\":6,\"right_edges\":[[0,2],[0,4],[1,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 0, 1, 1], 6, [0, 1, 1, 1, 1, 2], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 0, 1, 1], 6, [0, 1, 1, 1, 1, 2], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266077,"parameters":{"left_n":6,"left_edges":[[0,2]],"right_n":6,"right_edges":[[0,2],[0,4],[1,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,2]],\"left_n\":6,\"right_edges\":[[0,2],[0,4],[1,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0078","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,2]],\"right_n\":6,\"right_edges\":[[0,1],[0,2],[0,3],[0,4],[1,2],[1,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 2, 2, 3, 4], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 2, 2, 3, 4], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266078,"parameters":{"left_n":6,"left_edges":[[0,1],[0,2]],"right_n":6,"right_edges":[[0,1],[0,2],[0,3],[0,4],[1,2],[1,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,2]],\"left_n\":6,\"right_edges\":[[0,1],[0,2],[0,3],[0,4],[1,2],[1,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0079","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,3]],\"right_n\":6,\"right_edges\":[[0,3],[0,5],[1,4]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 0, 1, 1], 6, [0, 1, 1, 1, 1, 2], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 0, 1, 1], 6, [0, 1, 1, 1, 1, 2], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266079,"parameters":{"left_n":6,"left_edges":[[0,3]],"right_n":6,"right_edges":[[0,3],[0,5],[1,4]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,3]],\"left_n\":6,\"right_edges\":[[0,3],[0,5],[1,4]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0080","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,3]],\"right_n\":6,\"right_edges\":[[0,1],[0,4],[0,5],[1,2],[1,4]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 1, 2, 3, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 1, 2, 3, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266080,"parameters":{"left_n":6,"left_edges":[[0,1],[0,3]],"right_n":6,"right_edges":[[0,1],[0,4],[0,5],[1,2],[1,4]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,3]],\"left_n\":6,\"right_edges\":[[0,1],[0,4],[0,5],[1,2],[1,4]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0081","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,2],[0,3]],\"right_n\":6,\"right_edges\":[[0,2],[0,3],[0,4],[0,5],[1,3],[1,4]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [1, 1, 2, 2, 2, 4], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [1, 1, 2, 2, 2, 4], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266081,"parameters":{"left_n":6,"left_edges":[[0,2],[0,3]],"right_n":6,"right_edges":[[0,2],[0,3],[0,4],[0,5],[1,3],[1,4]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,2],[0,3]],\"left_n\":6,\"right_edges\":[[0,2],[0,3],[0,4],[0,5],[1,3],[1,4]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0082","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,2],[0,3]],\"right_n\":6,\"right_edges\":[[0,1],[0,2],[1,5]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 1, 1, 1, 3], 6, [0, 0, 1, 1, 2, 2], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 1, 1, 1, 3], 6, [0, 0, 1, 1, 2, 2], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266082,"parameters":{"left_n":6,"left_edges":[[0,1],[0,2],[0,3]],"right_n":6,"right_edges":[[0,1],[0,2],[1,5]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,2],[0,3]],\"left_n\":6,\"right_edges\":[[0,1],[0,2],[1,5]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0083","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,4]],\"right_n\":6,\"right_edges\":[[0,4],[1,2],[1,5]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 0, 1, 1], 6, [0, 1, 1, 1, 1, 2], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 0, 1, 1], 6, [0, 1, 1, 1, 1, 2], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266083,"parameters":{"left_n":6,"left_edges":[[0,4]],"right_n":6,"right_edges":[[0,4],[1,2],[1,5]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,4]],\"left_n\":6,\"right_edges\":[[0,4],[1,2],[1,5]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0084","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,4]],\"right_n\":6,\"right_edges\":[[0,1],[0,3],[0,4],[1,3],[1,5]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 1, 2, 3, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 1, 2, 3, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266084,"parameters":{"left_n":6,"left_edges":[[0,1],[0,4]],"right_n":6,"right_edges":[[0,1],[0,3],[0,4],[1,3],[1,5]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,4]],\"left_n\":6,\"right_edges\":[[0,1],[0,3],[0,4],[1,3],[1,5]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0085","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,2],[0,4]],\"right_n\":6,\"right_edges\":[[0,2],[0,5],[1,2],[1,3],[1,5]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 2, 2, 2, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 2, 2, 2, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266085,"parameters":{"left_n":6,"left_edges":[[0,2],[0,4]],"right_n":6,"right_edges":[[0,2],[0,5],[1,2],[1,3],[1,5]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,2],[0,4]],\"left_n\":6,\"right_edges\":[[0,2],[0,5],[1,2],[1,3],[1,5]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0086","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,2],[0,4]],\"right_n\":6,\"right_edges\":[[0,1],[0,2],[0,3],[0,5],[1,4],[1,5]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 2, 3, 4], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 2, 3, 4], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266086,"parameters":{"left_n":6,"left_edges":[[0,1],[0,2],[0,4]],"right_n":6,"right_edges":[[0,1],[0,2],[0,3],[0,5],[1,4],[1,5]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,2],[0,4]],\"left_n\":6,\"right_edges\":[[0,1],[0,2],[0,3],[0,5],[1,4],[1,5]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0087","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,3],[0,4]],\"right_n\":6,\"right_edges\":[[0,3],[0,4],[0,5],[1,2],[1,4],[1,5]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [1, 1, 2, 2, 3, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [1, 1, 2, 2, 3, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266087,"parameters":{"left_n":6,"left_edges":[[0,3],[0,4]],"right_n":6,"right_edges":[[0,3],[0,4],[0,5],[1,2],[1,4],[1,5]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,3],[0,4]],\"left_n\":6,\"right_edges\":[[0,3],[0,4],[0,5],[1,2],[1,4],[1,5]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0088","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,3],[0,4]],\"right_n\":6,\"right_edges\":[[0,1],[1,2],[1,3],[1,4],[1,5]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 1, 1, 5], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 1, 1, 5], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266088,"parameters":{"left_n":6,"left_edges":[[0,1],[0,3],[0,4]],"right_n":6,"right_edges":[[0,1],[1,2],[1,3],[1,4],[1,5]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,3],[0,4]],\"left_n\":6,\"right_edges\":[[0,1],[1,2],[1,3],[1,4],[1,5]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0089","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,2],[0,3],[0,4]],\"right_n\":6,\"right_edges\":[[0,2],[0,3],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 1, 1, 1, 3], 6, [0, 0, 0, 2, 2, 2], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 1, 1, 1, 3], 6, [0, 0, 0, 2, 2, 2], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266089,"parameters":{"left_n":6,"left_edges":[[0,2],[0,3],[0,4]],"right_n":6,"right_edges":[[0,2],[0,3],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,2],[0,3],[0,4]],\"left_n\":6,\"right_edges\":[[0,2],[0,3],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0090","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,2],[0,3],[0,4]],\"right_n\":6,\"right_edges\":[[0,1],[0,2],[0,4],[1,2],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 1, 1, 1, 4], 6, [0, 1, 1, 2, 3, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 1, 1, 1, 1, 4], 6, [0, 1, 1, 2, 3, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266090,"parameters":{"left_n":6,"left_edges":[[0,1],[0,2],[0,3],[0,4]],"right_n":6,"right_edges":[[0,1],[0,2],[0,4],[1,2],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,2],[0,3],[0,4]],\"left_n\":6,\"right_edges\":[[0,1],[0,2],[0,4],[1,2],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0091","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,5]],\"right_n\":6,\"right_edges\":[[0,5],[1,3],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 0, 1, 1], 6, [0, 1, 1, 1, 1, 2], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 0, 1, 1], 6, [0, 1, 1, 1, 1, 2], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266091,"parameters":{"left_n":6,"left_edges":[[0,5]],"right_n":6,"right_edges":[[0,5],[1,3],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,5]],\"left_n\":6,\"right_edges\":[[0,5],[1,3],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0092","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,5]],\"right_n\":6,\"right_edges\":[[0,1],[0,3],[0,5],[1,2],[1,3],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 2, 3, 3, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 2, 3, 3, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266092,"parameters":{"left_n":6,"left_edges":[[0,1],[0,5]],"right_n":6,"right_edges":[[0,1],[0,3],[0,5],[1,2],[1,3],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,5]],\"left_n\":6,\"right_edges\":[[0,1],[0,3],[0,5],[1,2],[1,3],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0093","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,2],[0,5]],\"right_n\":6,\"right_edges\":[[0,2],[0,4],[0,5],[1,4],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [1, 1, 1, 2, 2, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [1, 1, 1, 2, 2, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266093,"parameters":{"left_n":6,"left_edges":[[0,2],[0,5]],"right_n":6,"right_edges":[[0,2],[0,4],[0,5],[1,4],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,2],[0,5]],\"left_n\":6,\"right_edges\":[[0,2],[0,4],[0,5],[1,4],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0094","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,2],[0,5]],\"right_n\":6,\"right_edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,4],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 1, 1, 1, 3], 6, [1, 2, 2, 3, 3, 5], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 1, 1, 1, 3], 6, [1, 2, 2, 3, 3, 5], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266094,"parameters":{"left_n":6,"left_edges":[[0,1],[0,2],[0,5]],"right_n":6,"right_edges":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,4],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,2],[0,5]],\"left_n\":6,\"right_edges\":[[0,1],[0,2],[0,3],[0,4],[0,5],[1,2],[1,4],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0095","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,3],[0,5]],\"right_n\":6,\"right_edges\":[[0,3],[1,2],[1,3],[1,4],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 1, 2, 3, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [0, 1, 1, 2, 3, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266095,"parameters":{"left_n":6,"left_edges":[[0,3],[0,5]],"right_n":6,"right_edges":[[0,3],[1,2],[1,3],[1,4],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,3],[0,5]],\"left_n\":6,\"right_edges\":[[0,3],[1,2],[1,3],[1,4],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0096","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,3],[0,5]],\"right_n\":6,\"right_edges\":[[0,1],[0,4],[1,5],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 1, 2, 2], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 1, 1, 2, 2], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266096,"parameters":{"left_n":6,"left_edges":[[0,1],[0,3],[0,5]],"right_n":6,"right_edges":[[0,1],[0,4],[1,5],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,3],[0,5]],\"left_n\":6,\"right_edges\":[[0,1],[0,4],[1,5],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0097","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,2],[0,3],[0,5]],\"right_n\":6,\"right_edges\":[[0,2],[0,3],[0,4],[1,2],[1,5],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 2, 2, 3, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 1, 1, 1, 3], 6, [1, 1, 2, 2, 3, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266097,"parameters":{"left_n":6,"left_edges":[[0,2],[0,3],[0,5]],"right_n":6,"right_edges":[[0,2],[0,3],[0,4],[1,2],[1,5],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,2],[0,3],[0,5]],\"left_n\":6,\"right_edges\":[[0,2],[0,3],[0,4],[1,2],[1,5],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0098","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,2],[0,3],[0,5]],\"right_n\":6,\"right_edges\":[[0,1],[0,2],[0,5],[1,3],[1,5],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 1, 1, 1, 4], 6, [0, 2, 2, 2, 3, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 1, 1, 1, 1, 4], 6, [0, 2, 2, 2, 3, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266098,"parameters":{"left_n":6,"left_edges":[[0,1],[0,2],[0,3],[0,5]],"right_n":6,"right_edges":[[0,1],[0,2],[0,5],[1,3],[1,5],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,2],[0,3],[0,5]],\"left_n\":6,\"right_edges\":[[0,1],[0,2],[0,5],[1,3],[1,5],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0099","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,4],[0,5]],\"right_n\":6,\"right_edges\":[[0,4],[0,5],[1,2],[1,3],[1,5],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 0, 1, 1, 2], 6, [1, 2, 2, 2, 2, 3], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 0, 1, 1, 2], 6, [1, 2, 2, 2, 2, 3], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266099,"parameters":{"left_n":6,"left_edges":[[0,4],[0,5]],"right_n":6,"right_edges":[[0,4],[0,5],[1,2],[1,3],[1,5],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,4],[0,5]],\"left_n\":6,\"right_edges\":[[0,4],[0,5],[1,2],[1,3],[1,5],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261026-r06-graph-isomorphism-0100","batch_id":"batch-20261013-advance-20261026-r06-graph-isomorphism-foundations","language":"zh-Hant","source_mko_ids":["mko-graph-isomorphism"],"title_zh":"圖同構","stem_zh":"完整有限簡單圖與明示頂點映射。操作=graphiso-invariant-mismatch；資料={\"left_n\":6,\"left_edges\":[[0,1],[0,4],[0,5]],\"right_n\":6,\"right_edges\":[[0,1],[0,3],[0,4],[0,5],[1,4],[1,5],[2,3]]}。請依 [left_n,left_degree_multiset,right_n,right_degree_multiset,mismatch,conclusion] 欄序回答。","answer":{"kind":"expression","value":"(6, [0, 0, 1, 1, 1, 3], 6, [1, 2, 2, 2, 3, 4], 是, nonisomorphic_certificate)","explanation_zh":"結構深度核對=(6, [0, 0, 1, 1, 1, 3], 6, [1, 2, 2, 2, 3, 4], 是, nonisomorphic_certificate)；依完整明示資料重算；完整有限／精確切片不自動升格為任意無限定理；同構要求鄰接與非鄰接iff；不變量相同不足以證同構。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["圖同構"]},"variant":{"family_id":"qf-mod26-graphiso-invariant-mismatch","seed":202610266100,"parameters":{"left_n":6,"left_edges":[[0,1],[0,4],[0,5]],"right_n":6,"right_edges":[[0,1],[0,3],[0,4],[0,5],[1,4],[1,5],[2,3]],"domain":"Complete_finite_simple_graph_isomorphism","operation":"graphiso-invariant-mismatch","semantic_template":"qf-mod26-graphiso-invariant-mismatch/{\"left_edges\":[[0,1],[0,4],[0,5]],\"left_n\":6,\"right_edges\":[[0,1],[0,3],[0,4],[0,5],[1,4],[1,5],[2,3]],\"right_n\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、一般無限定理、獨立性、一般圖同構、不限維分析、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}