{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NM4WT7EB6TSIG2EQ5SCF3UCPAS","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":"9a5a526913bce05ce82ff91f5883f91d338085be9cfd582d6d376624c036c2f0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T18:17:12Z","title_canon_sha256":"407dd3f784b0cdc865f1fb17e568ab74272ab436b1a95a3cf00c7703ef397233"},"schema_version":"1.0","source":{"id":"1302.3829","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3829","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3829v2","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3829","created_at":"2026-05-18T02:43:09Z"},{"alias_kind":"pith_short_12","alias_value":"NM4WT7EB6TSI","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NM4WT7EB6TSIG2EQ","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NM4WT7EB","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:f6a313181adc3bdef14dfe84b7dcbb693ac7b642235c2a9a86faa2509842d8fa","target":"graph","created_at":"2026-05-18T02:43:09Z","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 study the Seifert surfaces of a link by relating the embeddings of graphs by using induced graphs. As applications, we prove that every link $L$ is the boundary of an oriented surface which is obtained from a graph embedding of a complete bipartite graph $K_{2,n}$, where all voltage assignments on the edges of $K_{2,n}$ are 0. We also provide an algorithm to construct such a graph diagram of a given link and demonstrate the algorithm by dealing with the links $4_1^2$ and $5_2$.","authors_text":"Dongseok Kim","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T18:17:12Z","title":"The boundaries of dipole graphs and the complete bipartite graphs K_{2,n}"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3829","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":"sha256:0146275e95f734a00c1ffe3a3fa3859f2374aa1ff73bc8021c923cefd5a7a950","target":"record","created_at":"2026-05-18T02:43:09Z","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":"9a5a526913bce05ce82ff91f5883f91d338085be9cfd582d6d376624c036c2f0","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T18:17:12Z","title_canon_sha256":"407dd3f784b0cdc865f1fb17e568ab74272ab436b1a95a3cf00c7703ef397233"},"schema_version":"1.0","source":{"id":"1302.3829","kind":"arxiv","version":2}},"canonical_sha256":"6b3969fc81f4e4836890ec845dd04f04bb464c08871f29c75a0b7a9789f68c8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b3969fc81f4e4836890ec845dd04f04bb464c08871f29c75a0b7a9789f68c8b","first_computed_at":"2026-05-18T02:43:09.497171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:09.497171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S8fxaYo9DHKJqId6M/6IFOV+hpI2HrX0d9Wtpji4jaWeskaP5c6wG62H+QqT9IggJho4yqx3qEjoN33KIgVWDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:09.497688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3829","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0146275e95f734a00c1ffe3a3fa3859f2374aa1ff73bc8021c923cefd5a7a950","sha256:f6a313181adc3bdef14dfe84b7dcbb693ac7b642235c2a9a86faa2509842d8fa"],"state_sha256":"6593db6991d4803e96e5dc20c12161da2ece0982805939016603ad933eba2c62"}