{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:W4KQFCI6QPPPR36FZ4QJQ4LUMS","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":"a53431776e2b6727fbaf0d6bfbac37625d7a6f7a208e43c2d8538496ed680985","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-16T16:24:45Z","title_canon_sha256":"359c03bef767584585b50b6a5f2a20ad5c968a7e270e4eae283796aa21286be7"},"schema_version":"1.0","source":{"id":"1511.05020","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.05020","created_at":"2026-05-18T01:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1511.05020v1","created_at":"2026-05-18T01:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.05020","created_at":"2026-05-18T01:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"W4KQFCI6QPPP","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"W4KQFCI6QPPPR36F","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"W4KQFCI6","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:151cc65bcd67204ca6a2bed78d9136e870ce7b389bf3cdc03cd69d38782f3442","target":"graph","created_at":"2026-05-18T01:26:51Z","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":"Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of $K_5$. This conjecture was proved by Ma and Yu for graphs containing $K_4^-$, and an important step in their proof is to deal with a 5-separation in the graph with a planar side. In order to establish the Kelmans-Seymour conjecture for all graphs, we need to consider 5-separations and 6-separations with less restrictive structures. The goal of this paper is to deal with special 5-separations and 6-separations, including those with an apex side. Results will be used in s","authors_text":"Dawei He, Xingxing Yu, Yan Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-16T16:24:45Z","title":"The Kelmans-Seymour conjecture I: special separations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05020","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":"sha256:2636bdc455aaf0a9437b00ecd16ffd8dbfd290000d70606aeac1a33540fcd1c1","target":"record","created_at":"2026-05-18T01:26:51Z","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":"a53431776e2b6727fbaf0d6bfbac37625d7a6f7a208e43c2d8538496ed680985","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-11-16T16:24:45Z","title_canon_sha256":"359c03bef767584585b50b6a5f2a20ad5c968a7e270e4eae283796aa21286be7"},"schema_version":"1.0","source":{"id":"1511.05020","kind":"arxiv","version":1}},"canonical_sha256":"b71502891e83def8efc5cf20987174649f6d222b129b4459d716aaebe0915be9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b71502891e83def8efc5cf20987174649f6d222b129b4459d716aaebe0915be9","first_computed_at":"2026-05-18T01:26:51.005360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:51.005360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xq1zvIyxe+hwaTApT9jMjbAvXcIT5oFB30GT455jUlF3LrBr7QNyOCranhTA6B4mzzOAXAI3WlyXD7dBdmyIDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:51.006119Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.05020","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2636bdc455aaf0a9437b00ecd16ffd8dbfd290000d70606aeac1a33540fcd1c1","sha256:151cc65bcd67204ca6a2bed78d9136e870ce7b389bf3cdc03cd69d38782f3442"],"state_sha256":"fe0b7f9e9028d75900e689c8316e54b956233d7da83f78ccbf8f7dbf889f9161"}