{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:7EDKJIRSQTNZVYA3IWHGT6SF6W","short_pith_number":"pith:7EDKJIRS","schema_version":"1.0","canonical_sha256":"f906a4a23284db9ae01b458e69fa45f5820e309effdc3a79a872a903255d0553","source":{"kind":"arxiv","id":"1012.5793","version":1},"attestation_state":"computed","paper":{"title":"The Kelmans-Seymour conjecture for apex graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elad Aigner-Horev, Roi Krakovski","submitted_at":"2010-12-28T16:59:15Z","abstract_excerpt":"We provide a short proof that a 5-connected nonplanar apex graph contains a subdivided $K_{_5}$ or a $K^-_{_4}$ (= $K_{_4}$ with a single edge removed) as a subgraph. Together with a recent result of Ma and Yu that {\\sl every nonplanar 5-connected graph containing $K^-_{_4}$ as a subgraph has a subdivided $K_{_5}$}; this settles the Kelmans-Seymour conjecture for apex graphs."},"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":"1012.5793","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-28T16:59:15Z","cross_cats_sorted":[],"title_canon_sha256":"433ac17b0827592fbe3b1a20a08dba13f74a584c3a96250838dc8c1dd9cf80d9","abstract_canon_sha256":"fc8995ab0966d7d7b11859ad5e06255a626899f14de6f8083b912cd2b66829fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:21.529390Z","signature_b64":"NWFhiT7fb4oVksibaf0eghT5BXW1weBfLq52gOEh+5XyGRT9HCxN7yrrMbAU8n9/SfggF3QTk9MK7rpTnnxQAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f906a4a23284db9ae01b458e69fa45f5820e309effdc3a79a872a903255d0553","last_reissued_at":"2026-05-18T04:32:21.528666Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:21.528666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Kelmans-Seymour conjecture for apex graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Elad Aigner-Horev, Roi Krakovski","submitted_at":"2010-12-28T16:59:15Z","abstract_excerpt":"We provide a short proof that a 5-connected nonplanar apex graph contains a subdivided $K_{_5}$ or a $K^-_{_4}$ (= $K_{_4}$ with a single edge removed) as a subgraph. Together with a recent result of Ma and Yu that {\\sl every nonplanar 5-connected graph containing $K^-_{_4}$ as a subgraph has a subdivided $K_{_5}$}; this settles the Kelmans-Seymour conjecture for apex graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5793","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":"1012.5793","created_at":"2026-05-18T04:32:21.528776+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.5793v1","created_at":"2026-05-18T04:32:21.528776+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5793","created_at":"2026-05-18T04:32:21.528776+00:00"},{"alias_kind":"pith_short_12","alias_value":"7EDKJIRSQTNZ","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_16","alias_value":"7EDKJIRSQTNZVYA3","created_at":"2026-05-18T12:26:04.259169+00:00"},{"alias_kind":"pith_short_8","alias_value":"7EDKJIRS","created_at":"2026-05-18T12:26:04.259169+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/7EDKJIRSQTNZVYA3IWHGT6SF6W","json":"https://pith.science/pith/7EDKJIRSQTNZVYA3IWHGT6SF6W.json","graph_json":"https://pith.science/api/pith-number/7EDKJIRSQTNZVYA3IWHGT6SF6W/graph.json","events_json":"https://pith.science/api/pith-number/7EDKJIRSQTNZVYA3IWHGT6SF6W/events.json","paper":"https://pith.science/paper/7EDKJIRS"},"agent_actions":{"view_html":"https://pith.science/pith/7EDKJIRSQTNZVYA3IWHGT6SF6W","download_json":"https://pith.science/pith/7EDKJIRSQTNZVYA3IWHGT6SF6W.json","view_paper":"https://pith.science/paper/7EDKJIRS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.5793&json=true","fetch_graph":"https://pith.science/api/pith-number/7EDKJIRSQTNZVYA3IWHGT6SF6W/graph.json","fetch_events":"https://pith.science/api/pith-number/7EDKJIRSQTNZVYA3IWHGT6SF6W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7EDKJIRSQTNZVYA3IWHGT6SF6W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7EDKJIRSQTNZVYA3IWHGT6SF6W/action/storage_attestation","attest_author":"https://pith.science/pith/7EDKJIRSQTNZVYA3IWHGT6SF6W/action/author_attestation","sign_citation":"https://pith.science/pith/7EDKJIRSQTNZVYA3IWHGT6SF6W/action/citation_signature","submit_replication":"https://pith.science/pith/7EDKJIRSQTNZVYA3IWHGT6SF6W/action/replication_record"}},"created_at":"2026-05-18T04:32:21.528776+00:00","updated_at":"2026-05-18T04:32:21.528776+00:00"}