{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ZHOJALNEJIGNPL6GWTXNJQYDDL","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":"cea92684ee4efdb45492616bf666d3147a6e963efc7cdceccf201dc240486990","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-27T13:12:28Z","title_canon_sha256":"fd3bef27d59b1995b84f8a4e0934fd58fe86cc3604ff77fb89e47fb3aa0282e9"},"schema_version":"1.0","source":{"id":"1101.5278","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5278","created_at":"2026-05-18T04:30:35Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5278v1","created_at":"2026-05-18T04:30:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5278","created_at":"2026-05-18T04:30:35Z"},{"alias_kind":"pith_short_12","alias_value":"ZHOJALNEJIGN","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"ZHOJALNEJIGNPL6G","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"ZHOJALNE","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:d563c507a28c687cd17ef37abbe350f7b291b95cd436bad804391802fe7a1283","target":"graph","created_at":"2026-05-18T04:30:35Z","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 first prove that for every vertex x of a 4-connected graph G there exists a subgraph H in G isomorphic to a subdivision of the complete graph K4 on four vertices such that G-V(H) is connected and contains x. This implies an affirmative answer to a question of W. Kuehnel whether every 4-connected graph G contains a subdivision H of K4 as a subgraph such that G-V(H) is connected. The motor for our induction is a result of Fontet and Martinov stating that every 4-connected graph can be reduced to a smaller one by contracting a single edge, unless the graph is the square of a cycle or the line ","authors_text":"Matthias Kriesell","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-27T13:12:28Z","title":"Nonseparating K4-subdivisions in graphs of minimum degree at least 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5278","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":"sha256:0cf0befeb53da3452203c8a5bd05f6ee8cba1334e19eb8fa265e61e7118ec175","target":"record","created_at":"2026-05-18T04:30:35Z","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":"cea92684ee4efdb45492616bf666d3147a6e963efc7cdceccf201dc240486990","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-27T13:12:28Z","title_canon_sha256":"fd3bef27d59b1995b84f8a4e0934fd58fe86cc3604ff77fb89e47fb3aa0282e9"},"schema_version":"1.0","source":{"id":"1101.5278","kind":"arxiv","version":1}},"canonical_sha256":"c9dc902da44a0cd7afc6b4eed4c3031aee7e017b19706ad53315dc3b450d7b75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9dc902da44a0cd7afc6b4eed4c3031aee7e017b19706ad53315dc3b450d7b75","first_computed_at":"2026-05-18T04:30:35.784893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:35.784893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9hGOy8uQBY4Q62tqkxY5yAGjbRJKc9xjCL7F/Bjct4EN1pItVvcVGWG1T2lZF8vytjGh4vuhFW2uzbXz9bWjAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:35.785499Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.5278","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cf0befeb53da3452203c8a5bd05f6ee8cba1334e19eb8fa265e61e7118ec175","sha256:d563c507a28c687cd17ef37abbe350f7b291b95cd436bad804391802fe7a1283"],"state_sha256":"d925c34ca7bae093c0ed7c060362f31f88a2260628ae3697476deb8e4a3c1365"}