{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TSU37G6OGHSBFCUTVIDVR7DYUM","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":"6dc71013841d92bfb74e96a66b341e212f8a775d40675b567a8322466e95efb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-24T07:06:23Z","title_canon_sha256":"2db9958c327897e1864278ec9a508b5f648fd4fc08d11162e6d5f448e6940687"},"schema_version":"1.0","source":{"id":"1405.6272","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.6272","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"1405.6272v3","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.6272","created_at":"2026-05-18T02:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"TSU37G6OGHSB","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"TSU37G6OGHSBFCUT","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"TSU37G6O","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:22abf8de0ace30119b75f87aa657bc2480f13e5952db4f33b216595101de5cf0","target":"graph","created_at":"2026-05-18T02:25:04Z","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":"In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of paths of lengths 6 and 7 those contain a specific vertex $v_{i}$ in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.","authors_text":"Nazanin Movarraei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-24T07:06:23Z","title":"On the Number of cycles in a Graph"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6272","kind":"arxiv","version":3},"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:eb6e3279f528c858b9e3f515a33a7b1d0c2f324d036a5148eeb0fb1dc837201c","target":"record","created_at":"2026-05-18T02:25:04Z","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":"6dc71013841d92bfb74e96a66b341e212f8a775d40675b567a8322466e95efb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-24T07:06:23Z","title_canon_sha256":"2db9958c327897e1864278ec9a508b5f648fd4fc08d11162e6d5f448e6940687"},"schema_version":"1.0","source":{"id":"1405.6272","kind":"arxiv","version":3}},"canonical_sha256":"9ca9bf9bce31e4128a93aa0758fc78a330f41b6f2716c2d416a3f2ed1463ad2a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ca9bf9bce31e4128a93aa0758fc78a330f41b6f2716c2d416a3f2ed1463ad2a","first_computed_at":"2026-05-18T02:25:04.774691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:04.774691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iiVuV2VLG4gaJ/qCsPd5jEH4kGamnB+8+WVY0W5BnUtxHovSqmt2Otd9m2ZkhS+ys1NyWxY7PKahMtThzEBfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:04.775069Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.6272","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb6e3279f528c858b9e3f515a33a7b1d0c2f324d036a5148eeb0fb1dc837201c","sha256:22abf8de0ace30119b75f87aa657bc2480f13e5952db4f33b216595101de5cf0"],"state_sha256":"80e38f1f489f362325eada618da00cf3c35b2aa3c0e4791a57808fab5963f4bc"}