{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7EDKJIRSQTNZVYA3IWHGT6SF6W","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fc8995ab0966d7d7b11859ad5e06255a626899f14de6f8083b912cd2b66829fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-28T16:59:15Z","title_canon_sha256":"433ac17b0827592fbe3b1a20a08dba13f74a584c3a96250838dc8c1dd9cf80d9"},"schema_version":"1.0","source":{"id":"1012.5793","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.5793","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"arxiv_version","alias_value":"1012.5793v1","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5793","created_at":"2026-05-18T04:32:21Z"},{"alias_kind":"pith_short_12","alias_value":"7EDKJIRSQTNZ","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7EDKJIRSQTNZVYA3","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7EDKJIRS","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:95d04fa0b89866a76dcb09e21da9b164193e10a9cae988005dd46c98d29b3274","target":"graph","created_at":"2026-05-18T04:32:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Elad Aigner-Horev, Roi Krakovski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-28T16:59:15Z","title":"The Kelmans-Seymour conjecture for apex graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5793","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:78058e9a7593d9f647353f608cdbce36082097f7ebb6d171b3804fcaf8a6336e","target":"record","created_at":"2026-05-18T04:32:21Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fc8995ab0966d7d7b11859ad5e06255a626899f14de6f8083b912cd2b66829fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-28T16:59:15Z","title_canon_sha256":"433ac17b0827592fbe3b1a20a08dba13f74a584c3a96250838dc8c1dd9cf80d9"},"schema_version":"1.0","source":{"id":"1012.5793","kind":"arxiv","version":1}},"canonical_sha256":"f906a4a23284db9ae01b458e69fa45f5820e309effdc3a79a872a903255d0553","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f906a4a23284db9ae01b458e69fa45f5820e309effdc3a79a872a903255d0553","first_computed_at":"2026-05-18T04:32:21.528666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:32:21.528666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NWFhiT7fb4oVksibaf0eghT5BXW1weBfLq52gOEh+5XyGRT9HCxN7yrrMbAU8n9/SfggF3QTk9MK7rpTnnxQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:32:21.529390Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.5793","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78058e9a7593d9f647353f608cdbce36082097f7ebb6d171b3804fcaf8a6336e","sha256:95d04fa0b89866a76dcb09e21da9b164193e10a9cae988005dd46c98d29b3274"],"state_sha256":"6d69ff9322240eb1b565b20002e5ef9c1c33c1ee290cfc0c430eca217fa8c4de"}