{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:QCZ4PHMHPAPSTTDZJDM7F4TDHS","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":"5eae9318bec62e72b368a3bdda781827c821771f0d766b5001f42b05ef06bd92","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-02-07T10:52:36Z","title_canon_sha256":"100f7c4557e2c485afcfab880d23552494b001be6459bd01fd25701b11405af3"},"schema_version":"1.0","source":{"id":"2202.03061","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.03061","created_at":"2026-07-05T03:54:35Z"},{"alias_kind":"arxiv_version","alias_value":"2202.03061v1","created_at":"2026-07-05T03:54:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.03061","created_at":"2026-07-05T03:54:35Z"},{"alias_kind":"pith_short_12","alias_value":"QCZ4PHMHPAPS","created_at":"2026-07-05T03:54:35Z"},{"alias_kind":"pith_short_16","alias_value":"QCZ4PHMHPAPSTTDZ","created_at":"2026-07-05T03:54:35Z"},{"alias_kind":"pith_short_8","alias_value":"QCZ4PHMH","created_at":"2026-07-05T03:54:35Z"}],"graph_snapshots":[{"event_id":"sha256:4d04a4ef5a7bc45b4be30a642816e49a566f8c77d998fd146662c8f620dee157","target":"graph","created_at":"2026-07-05T03:54:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2202.03061/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In 1959, Erd\\H{o}s and Gallai proved that every graph G with average vertex degree ad(G)\\geq 2 contains a cycle of length at least ad(G). We provide an algorithm that for k\\geq 0 in time 2^{O(k)} n^{O(1)} decides whether a 2-connected n-vertex graph G contains a cycle of length at least ad(G)+k. This resolves an open problem explicitly mentioned in several papers. The main ingredients of our algorithm are new graph-theoretical results interesting on their own.","authors_text":"Danil Sagunov, Fedor V. Fomin, Kirill Simonov, Petr A. Golovach","cross_cats":["cs.DM","math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-02-07T10:52:36Z","title":"Longest Cycle above Erd\\H{o}s-Gallai Bound"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.03061","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":"sha256:50783a4d0cbc168e05f7b10732efdc2d417bf46e67d8d69f8e64d4ae3475d163","target":"record","created_at":"2026-07-05T03:54:35Z","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":"5eae9318bec62e72b368a3bdda781827c821771f0d766b5001f42b05ef06bd92","cross_cats_sorted":["cs.DM","math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2022-02-07T10:52:36Z","title_canon_sha256":"100f7c4557e2c485afcfab880d23552494b001be6459bd01fd25701b11405af3"},"schema_version":"1.0","source":{"id":"2202.03061","kind":"arxiv","version":1}},"canonical_sha256":"80b3c79d87781f29cc7948d9f2f2633ca9caca42c1843cb95283f77768ef7c6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80b3c79d87781f29cc7948d9f2f2633ca9caca42c1843cb95283f77768ef7c6b","first_computed_at":"2026-07-05T03:54:35.307541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:54:35.307541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hmGgwNLGjjHe7cXrcNhf1zOvbGwD2E+hM/7zIpbzaTmY0tj1hFrj08hANM2NOlZD/U5zid1rDQ0w/NDV4gNfBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:54:35.307910Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.03061","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50783a4d0cbc168e05f7b10732efdc2d417bf46e67d8d69f8e64d4ae3475d163","sha256:4d04a4ef5a7bc45b4be30a642816e49a566f8c77d998fd146662c8f620dee157"],"state_sha256":"8e90369fa3e8e2789f445fcc9f92f6ddfe67229a054f1b700a2e3e9a7c3c187b"}