{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:XAVE3VUBI3ZTOEZFIW2YZK2V73","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":"e4f8ec8e699b25e549384685757edb790b63508483cba270bf4ac87ed3adb206","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-30T10:02:29Z","title_canon_sha256":"dfa0e7ab65bb53b6664088ab2426ca437ef2443e7dac4511cca0c444a67a2b1f"},"schema_version":"1.0","source":{"id":"1307.0192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0192","created_at":"2026-05-18T03:19:34Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0192v1","created_at":"2026-05-18T03:19:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0192","created_at":"2026-05-18T03:19:34Z"},{"alias_kind":"pith_short_12","alias_value":"XAVE3VUBI3ZT","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"XAVE3VUBI3ZTOEZF","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"XAVE3VUB","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:1305c7c7a9ed2d7a209a1c1b4408b85d0ec5d9bbc4cb3c206c20ae83dc1081b0","target":"graph","created_at":"2026-05-18T03:19:34Z","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":"The revised Szeged index of a graph $G$ is defined as $Sz^*(G)=\\sum_{e=uv \\in E}(n_u(e)+ n_0(e)/2)(n_v(e)+ n_0(e)/2),$ where $n_u(e)$ and $n_v(e)$ are, respectively, the number of vertices of $G$ lying closer to vertex $u$ than to vertex $v$ and the number of vertices of $G$ lying closer to vertex $v$ than to vertex $u$, and $n_0(e)$ is the number of vertices equidistant to $u$ and $v$. In this paper, we give an upper bound of the revised Szeged index for a connected tricyclic graph, and also characterize those graphs that achieve the upper bound.","authors_text":"Lily Chen, Mengmeng Liu, Xueliang Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-30T10:02:29Z","title":"Tricyclic graphs with maximal revised Szeged index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0192","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":"sha256:80db0a7e5eca954b74bc2b20ab56d277d5da9afbd2817a8c8f65b55dda28d13e","target":"record","created_at":"2026-05-18T03:19:34Z","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":"e4f8ec8e699b25e549384685757edb790b63508483cba270bf4ac87ed3adb206","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-06-30T10:02:29Z","title_canon_sha256":"dfa0e7ab65bb53b6664088ab2426ca437ef2443e7dac4511cca0c444a67a2b1f"},"schema_version":"1.0","source":{"id":"1307.0192","kind":"arxiv","version":1}},"canonical_sha256":"b82a4dd68146f337132545b58cab55feec45f96036c71791a05b0e854b128e04","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b82a4dd68146f337132545b58cab55feec45f96036c71791a05b0e854b128e04","first_computed_at":"2026-05-18T03:19:34.020249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:34.020249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FmvhnivZBqF1WBysXwPpJF6qvRONfsgF13p+t26MfoF2JWsTrWWZQJ8Rm6cxp93L4Sy6IzF3vqgKLNql/50EAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:34.020772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80db0a7e5eca954b74bc2b20ab56d277d5da9afbd2817a8c8f65b55dda28d13e","sha256:1305c7c7a9ed2d7a209a1c1b4408b85d0ec5d9bbc4cb3c206c20ae83dc1081b0"],"state_sha256":"4a8027769ccbc88b363b962b71af27710f0fca34202936d2060bf5bf97465dfb"}