{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:GBTGNF3CLGGAU3Y5LB2NH3MR3I","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":"15cdc71a5dfdd47fd270fd81d69d6dd405480e7129223e54031fae288f9869bc","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-11-28T01:00:01Z","title_canon_sha256":"3c1b18b8d04c384972874d492a4f717dee717982cbf4ead8ab73523d034a5a6a"},"schema_version":"1.0","source":{"id":"0711.4394","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0711.4394","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"arxiv_version","alias_value":"0711.4394v2","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0711.4394","created_at":"2026-05-18T04:09:04Z"},{"alias_kind":"pith_short_12","alias_value":"GBTGNF3CLGGA","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"GBTGNF3CLGGAU3Y5","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"GBTGNF3C","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:31d5c91a8100f367e2df37cd5ffac362df93c917de325458e85e32937d05e8df","target":"graph","created_at":"2026-05-18T04:09:04Z","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 conjecture that a 2-connected graph $G$ of order $n$, in which $d(x)+d(y)\\geq n-k$ for every pair of non-adjacent vertices $x$ and $y$, contains a cycle of length $n-k$ ($k<n/2$), unless $G$ is bipartite and $n-k$ is odd. This generalizes to long cycles a well-known degree sum condition for hamiltonicity of Ore. The conjecture is shown to hold for $k=1$.","authors_text":"Janusz Adamus","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2007-11-28T01:00:01Z","title":"A note on a degree sum condition for long cycles in graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0711.4394","kind":"arxiv","version":2},"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":"sha256:7586f5f7c93e373c2fb4ccfd10a5ce6f231f158ab3dffb14142205a3b8a29bc3","target":"record","created_at":"2026-05-18T04:09:04Z","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":"15cdc71a5dfdd47fd270fd81d69d6dd405480e7129223e54031fae288f9869bc","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-11-28T01:00:01Z","title_canon_sha256":"3c1b18b8d04c384972874d492a4f717dee717982cbf4ead8ab73523d034a5a6a"},"schema_version":"1.0","source":{"id":"0711.4394","kind":"arxiv","version":2}},"canonical_sha256":"3066669762598c0a6f1d5874d3ed91da2e60398c1b56da4cbc8b6dde90aa4347","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3066669762598c0a6f1d5874d3ed91da2e60398c1b56da4cbc8b6dde90aa4347","first_computed_at":"2026-05-18T04:09:04.471309Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:04.471309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NbrBenj7HWzxO7Ghap/kBzkQU9Xh9LqRu7CduMqimuORujjoE/3+AWbn06uN1x3QEesy4/npaTi0AIPdTGSTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:04.471998Z","signed_message":"canonical_sha256_bytes"},"source_id":"0711.4394","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7586f5f7c93e373c2fb4ccfd10a5ce6f231f158ab3dffb14142205a3b8a29bc3","sha256:31d5c91a8100f367e2df37cd5ffac362df93c917de325458e85e32937d05e8df"],"state_sha256":"60bf8ce51a67f8b49782cdf167b9de1de4f6033fe45b8dbd6e879341c2c9a148"}