{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:74YBX3ZHE5OSMBOBIZ7TMUSVJM","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":"746ef87400df90ab449c56f7a136175d2aabf7064fd2fef2867c55e0c53bee8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-24T08:48:55Z","title_canon_sha256":"af8cf759f44033b7df2546029bc396a7b0a4ff9fa3d7e0fc84902d0fbdcf14d3"},"schema_version":"1.0","source":{"id":"1210.6460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.6460","created_at":"2026-05-18T03:42:24Z"},{"alias_kind":"arxiv_version","alias_value":"1210.6460v1","created_at":"2026-05-18T03:42:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.6460","created_at":"2026-05-18T03:42:24Z"},{"alias_kind":"pith_short_12","alias_value":"74YBX3ZHE5OS","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"74YBX3ZHE5OSMBOB","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"74YBX3ZH","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:2cc55d6b0735ec18d4fcd4e10309bdae359bd15d2d843e94ff406d9cdeb81c94","target":"graph","created_at":"2026-05-18T03:42:24Z","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":"{\\small The Wiener index $W(G)$ of a graph $G$ is the sum of the distances between all pairs of vertices in the graph. The Szeged index $Sz(G)$ of a graph $G$ is defined as $Sz(G)=\\sum_{e=uv \\in E}n_u(e)n_v(e)$ 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 $u$. Hansen used the computer programm AutoGraphiX and made the following conjecture about the Szeged index and the Wiener index for a bipartite connected graph $G$ with $n \\geq 4$ vertices ","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":"2012-10-24T08:48:55Z","title":"On a relation between the Szeged index and the Wiener index for bipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.6460","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:fccef0060e97eb292da30eb2c29ca72a252759b63b75af19ef6dbbf772dca7cb","target":"record","created_at":"2026-05-18T03:42:24Z","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":"746ef87400df90ab449c56f7a136175d2aabf7064fd2fef2867c55e0c53bee8c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-24T08:48:55Z","title_canon_sha256":"af8cf759f44033b7df2546029bc396a7b0a4ff9fa3d7e0fc84902d0fbdcf14d3"},"schema_version":"1.0","source":{"id":"1210.6460","kind":"arxiv","version":1}},"canonical_sha256":"ff301bef27275d2605c1467f3652554b08dc418af8ecf2da41fb3633e81d6613","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff301bef27275d2605c1467f3652554b08dc418af8ecf2da41fb3633e81d6613","first_computed_at":"2026-05-18T03:42:24.775722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:42:24.775722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EJgM41mksxfYhv6XVN2Xl1KhEMf8btyPIDUNe2pq6NLojqflNqZTVKn+FFDwNsn5Z2v+dAhVzaOm8XNTMVNPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:42:24.776461Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.6460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fccef0060e97eb292da30eb2c29ca72a252759b63b75af19ef6dbbf772dca7cb","sha256:2cc55d6b0735ec18d4fcd4e10309bdae359bd15d2d843e94ff406d9cdeb81c94"],"state_sha256":"3b970a604f0a79385188b14ab94395ff342de975c89ca7a5d9415e91f7f4ab53"}