{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B6HL5WF5GDGHARCQKV6BP3XJ6W","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":"4939ab2306af4a4f539adf357264b4f357bede0b8a18ccdfa21417a4c78d273f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-30T13:13:10Z","title_canon_sha256":"c48faeb46b81b4f58791858fb3c7050d641e5abcda6e6f425e23c21a3135fabe"},"schema_version":"1.0","source":{"id":"1407.8031","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.8031","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"arxiv_version","alias_value":"1407.8031v1","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.8031","created_at":"2026-05-18T02:46:13Z"},{"alias_kind":"pith_short_12","alias_value":"B6HL5WF5GDGH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"B6HL5WF5GDGHARCQ","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"B6HL5WF5","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:6550be32e6106d7771472c0cbf1b380d5ad77abd4e02fe612e650fe826f1420a","target":"graph","created_at":"2026-05-18T02:46:13Z","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 derive a quadratic-time algorithm for the genus distribution of any 3-regular, biconnected series-parallel graph, which we extend to any biconnected series-parallel graph of maximum degree at most 3. Since the biconnected components of every graph of treewidth 2 are series-parallel graphs, this yields, by use of bar-amalgamation, a quadratic-time algorithm for every graph of treewidth at most 2 and maximum degree at most 3.","authors_text":"Jonathan L. Gross, Michal Kotrb\\v{c}\\'ik, Timothy Sun","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-30T13:13:10Z","title":"Genus Distributions of cubic series-parallel graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.8031","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":"sha256:032eef830a3fbd3ecd3f868089de34bbc3fd845ad25661a42cbb5d1868bb2bd3","target":"record","created_at":"2026-05-18T02:46:13Z","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":"4939ab2306af4a4f539adf357264b4f357bede0b8a18ccdfa21417a4c78d273f","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-07-30T13:13:10Z","title_canon_sha256":"c48faeb46b81b4f58791858fb3c7050d641e5abcda6e6f425e23c21a3135fabe"},"schema_version":"1.0","source":{"id":"1407.8031","kind":"arxiv","version":1}},"canonical_sha256":"0f8ebed8bd30cc704450557c17eee9f58e87ee2be08b91cfb6148dff304a65ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f8ebed8bd30cc704450557c17eee9f58e87ee2be08b91cfb6148dff304a65ae","first_computed_at":"2026-05-18T02:46:13.781892Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:13.781892Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v668ZMu98x6XpCf+cNGgcK5PDoWNb4uEtnAzokv16IEIlQ2p1OTZw48aXsXOYvvbSI9WeVRJF7uvP4KeHUHGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:13.782944Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.8031","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:032eef830a3fbd3ecd3f868089de34bbc3fd845ad25661a42cbb5d1868bb2bd3","sha256:6550be32e6106d7771472c0cbf1b380d5ad77abd4e02fe612e650fe826f1420a"],"state_sha256":"513d56d1dd7665e9597496596e0c89e3d969af6a432a7af2b2d5ce835dbaa111"}