{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6GSU45VLDHNSGEVHRO44OZRH2H","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":"286696336837a762128b2aca746ee511a0c27449724a6943cbb42ce4f006a937","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-26T16:57:46Z","title_canon_sha256":"bb72e3eab3adbaa41e2222d60cc7bd063f710caaf0781c14bef1b0ff59f39cbd"},"schema_version":"1.0","source":{"id":"1308.5638","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.5638","created_at":"2026-05-18T03:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"1308.5638v1","created_at":"2026-05-18T03:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5638","created_at":"2026-05-18T03:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"6GSU45VLDHNS","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6GSU45VLDHNSGEVH","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6GSU45VL","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:153b08d1310b4162392e7c2e0831226ca4dcfd88bf2c2c1f370d94ca5398349c","target":"graph","created_at":"2026-05-18T03:15:03Z","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 splitting number of a link is the minimal number of crossing changes between different components required, on any diagram, to convert it to a split link. We introduce new techniques to compute the splitting number, involving covering links and Alexander invariants. As an application, we completely determine the splitting numbers of links with 9 or fewer crossings. Also, with these techniques, we either reprove or improve upon the lower bounds for splitting numbers of links computed by J. Batson and C. Seed using Khovanov homology.","authors_text":"Jae Choon Cha, Mark Powell, Stefan Friedl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-26T16:57:46Z","title":"Splitting numbers of links"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5638","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:dca08dc413427015324937f76f8e43e6428f22ca7e770dc4d959e07f05ca2ec1","target":"record","created_at":"2026-05-18T03:15:03Z","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":"286696336837a762128b2aca746ee511a0c27449724a6943cbb42ce4f006a937","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-08-26T16:57:46Z","title_canon_sha256":"bb72e3eab3adbaa41e2222d60cc7bd063f710caaf0781c14bef1b0ff59f39cbd"},"schema_version":"1.0","source":{"id":"1308.5638","kind":"arxiv","version":1}},"canonical_sha256":"f1a54e76ab19db2312a78bb9c76627d1e59c43518d300f6b9db4fe414cf487e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1a54e76ab19db2312a78bb9c76627d1e59c43518d300f6b9db4fe414cf487e6","first_computed_at":"2026-05-18T03:15:03.930134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:03.930134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"90WfCs/vGoULF1ECiUQgWXHB9gpK49Us3aHvedC7QTsz5qsOaQMYdpqaS+uaMWtISCoLVP9zQw/Mf/tfQzYtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:03.930916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.5638","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dca08dc413427015324937f76f8e43e6428f22ca7e770dc4d959e07f05ca2ec1","sha256:153b08d1310b4162392e7c2e0831226ca4dcfd88bf2c2c1f370d94ca5398349c"],"state_sha256":"ef8c9f490f5e7fccaea7bcfce42307176b496fe3a5951bac716156d18ee7192d"}