{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:XUMUW3IFL2H57EFVNMULJXKDAP","short_pith_number":"pith:XUMUW3IF","schema_version":"1.0","canonical_sha256":"bd194b6d055e8fdf90b56b28b4dd4303d7353a8a83b7956c51cc241befbdcc87","source":{"kind":"arxiv","id":"1602.07557","version":1},"attestation_state":"computed","paper":{"title":"The Kelmans-Seymour conjecture II: 2-vertices in $K_4^-$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dawei He, Xingxing Yu, Yan Wang","submitted_at":"2016-02-24T15:27:02Z","abstract_excerpt":"We use $K_4^-$ to denote the graph obtained from $K_4$ by removing an edge, and use $TK_5$ to denote a subdivision of $K_5$. Let $G$ be a 5-connected nonplanar graph and $\\{x_1,x_2,y_1,y_2\\}\\subseteq V(G)$ such that $G[\\{x_1,x_2,$ $y_1,y_2\\}]\\cong K_4^-$ with $y_1y_2\\notin E(G)$. Let $w_1,w_2,w_3\\in N(y_2)-\\{x_1,x_2\\}$ be distinct. We show that $G$ contains a $TK_5$ in which $y_2$ is not a branch vertex, or $G-y_2$ contains $K_4^-$, or $G$ has a special 5-separation, or $G-\\{y_2v:v\\notin \\{w_1,w_2,w_3,x_1,x_2\\}\\}$ contains $TK_5$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1602.07557","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-02-24T15:27:02Z","cross_cats_sorted":[],"title_canon_sha256":"dea12b7cfe244cf5e91f354c30586899b70042c8ac17f80057e0aa55900bd275","abstract_canon_sha256":"d576c460b97ede0026ebccf4e6f00deb5d62492d773fa53ef9ec3f6a7ed584e1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:02.655270Z","signature_b64":"5a5wA3VSGqv08DzlK/iavAOPpf/WSQinhNIvKkzm+SEbrFKXrO//ZoV/8yuiEfTjkXkt9tvikg1sjPT/+1H5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd194b6d055e8fdf90b56b28b4dd4303d7353a8a83b7956c51cc241befbdcc87","last_reissued_at":"2026-05-18T01:20:02.654569Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:02.654569Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Kelmans-Seymour conjecture II: 2-vertices in $K_4^-$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dawei He, Xingxing Yu, Yan Wang","submitted_at":"2016-02-24T15:27:02Z","abstract_excerpt":"We use $K_4^-$ to denote the graph obtained from $K_4$ by removing an edge, and use $TK_5$ to denote a subdivision of $K_5$. Let $G$ be a 5-connected nonplanar graph and $\\{x_1,x_2,y_1,y_2\\}\\subseteq V(G)$ such that $G[\\{x_1,x_2,$ $y_1,y_2\\}]\\cong K_4^-$ with $y_1y_2\\notin E(G)$. Let $w_1,w_2,w_3\\in N(y_2)-\\{x_1,x_2\\}$ be distinct. We show that $G$ contains a $TK_5$ in which $y_2$ is not a branch vertex, or $G-y_2$ contains $K_4^-$, or $G$ has a special 5-separation, or $G-\\{y_2v:v\\notin \\{w_1,w_2,w_3,x_1,x_2\\}\\}$ contains $TK_5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07557","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1602.07557","created_at":"2026-05-18T01:20:02.654687+00:00"},{"alias_kind":"arxiv_version","alias_value":"1602.07557v1","created_at":"2026-05-18T01:20:02.654687+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.07557","created_at":"2026-05-18T01:20:02.654687+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUMUW3IFL2H5","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUMUW3IFL2H57EFV","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUMUW3IF","created_at":"2026-05-18T12:30:51.357362+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/XUMUW3IFL2H57EFVNMULJXKDAP","json":"https://pith.science/pith/XUMUW3IFL2H57EFVNMULJXKDAP.json","graph_json":"https://pith.science/api/pith-number/XUMUW3IFL2H57EFVNMULJXKDAP/graph.json","events_json":"https://pith.science/api/pith-number/XUMUW3IFL2H57EFVNMULJXKDAP/events.json","paper":"https://pith.science/paper/XUMUW3IF"},"agent_actions":{"view_html":"https://pith.science/pith/XUMUW3IFL2H57EFVNMULJXKDAP","download_json":"https://pith.science/pith/XUMUW3IFL2H57EFVNMULJXKDAP.json","view_paper":"https://pith.science/paper/XUMUW3IF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1602.07557&json=true","fetch_graph":"https://pith.science/api/pith-number/XUMUW3IFL2H57EFVNMULJXKDAP/graph.json","fetch_events":"https://pith.science/api/pith-number/XUMUW3IFL2H57EFVNMULJXKDAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUMUW3IFL2H57EFVNMULJXKDAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUMUW3IFL2H57EFVNMULJXKDAP/action/storage_attestation","attest_author":"https://pith.science/pith/XUMUW3IFL2H57EFVNMULJXKDAP/action/author_attestation","sign_citation":"https://pith.science/pith/XUMUW3IFL2H57EFVNMULJXKDAP/action/citation_signature","submit_replication":"https://pith.science/pith/XUMUW3IFL2H57EFVNMULJXKDAP/action/replication_record"}},"created_at":"2026-05-18T01:20:02.654687+00:00","updated_at":"2026-05-18T01:20:02.654687+00:00"}