{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NM4WT7EB6TSIG2EQ5SCF3UCPAS","short_pith_number":"pith:NM4WT7EB","canonical_record":{"source":{"id":"1302.3829","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T18:17:12Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"407dd3f784b0cdc865f1fb17e568ab74272ab436b1a95a3cf00c7703ef397233","abstract_canon_sha256":"9a5a526913bce05ce82ff91f5883f91d338085be9cfd582d6d376624c036c2f0"},"schema_version":"1.0"},"canonical_sha256":"6b3969fc81f4e4836890ec845dd04f04bb464c08871f29c75a0b7a9789f68c8b","source":{"kind":"arxiv","id":"1302.3829","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NM4WT7EB6TSIG2EQ5SCF3UCPAS","target":"record","payload":{"canonical_record":{"source":{"id":"1302.3829","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-02-15T18:17:12Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"407dd3f784b0cdc865f1fb17e568ab74272ab436b1a95a3cf00c7703ef397233","abstract_canon_sha256":"9a5a526913bce05ce82ff91f5883f91d338085be9cfd582d6d376624c036c2f0"},"schema_version":"1.0"},"canonical_sha256":"6b3969fc81f4e4836890ec845dd04f04bb464c08871f29c75a0b7a9789f68c8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:09.497688Z","signature_b64":"S8fxaYo9DHKJqId6M/6IFOV+hpI2HrX0d9Wtpji4jaWeskaP5c6wG62H+QqT9IggJho4yqx3qEjoN33KIgVWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b3969fc81f4e4836890ec845dd04f04bb464c08871f29c75a0b7a9789f68c8b","last_reissued_at":"2026-05-18T02:43:09.497171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:09.497171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.3829","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38aGyMOPF5MxQN1G1oCHdHzFc5fivEvk4dhYKSPjhJt2MpEJn40WkXZeHMfWt53g/HCr+C25N2Mo6r2WWXD9AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:32:09.468769Z"},"content_sha256":"0146275e95f734a00c1ffe3a3fa3859f2374aa1ff73bc8021c923cefd5a7a950","schema_version":"1.0","event_id":"sha256:0146275e95f734a00c1ffe3a3fa3859f2374aa1ff73bc8021c923cefd5a7a950"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NM4WT7EB6TSIG2EQ5SCF3UCPAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The boundaries of dipole graphs and the complete bipartite graphs K_{2,n}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GT","authors_text":"Dongseok Kim","submitted_at":"2013-02-15T18:17:12Z","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 $5_2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3829","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:43:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6tUK3C2M4dGPJmSxKuSaHdrf5bKZ92jvqPunYu+zxNOkxtYDrSazLEk5exVrpWkOETTqeO3AxMF9LdSEEEkCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T23:32:09.469440Z"},"content_sha256":"f6a313181adc3bdef14dfe84b7dcbb693ac7b642235c2a9a86faa2509842d8fa","schema_version":"1.0","event_id":"sha256:f6a313181adc3bdef14dfe84b7dcbb693ac7b642235c2a9a86faa2509842d8fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NM4WT7EB6TSIG2EQ5SCF3UCPAS/bundle.json","state_url":"https://pith.science/pith/NM4WT7EB6TSIG2EQ5SCF3UCPAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NM4WT7EB6TSIG2EQ5SCF3UCPAS/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-18T23:32:09Z","links":{"resolver":"https://pith.science/pith/NM4WT7EB6TSIG2EQ5SCF3UCPAS","bundle":"https://pith.science/pith/NM4WT7EB6TSIG2EQ5SCF3UCPAS/bundle.json","state":"https://pith.science/pith/NM4WT7EB6TSIG2EQ5SCF3UCPAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NM4WT7EB6TSIG2EQ5SCF3UCPAS/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WCmkrBtHnCb0ITLmHv62jq6wLVX2Mw3U03FdO1D5zJ/nvnydwg13AuFrMF1cxWHJy7aiJtpX02tNi7viHwI+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T23:32:09.471351Z","bundle_sha256":"9dd6acf1672ac5cad0e7bc450f317f703be51f8aae944848d3ee5a8dab456c25"}}