{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ETG2KBE3PPPMLMTWDBRJPOE54T","short_pith_number":"pith:ETG2KBE3","schema_version":"1.0","canonical_sha256":"24cda5049b7bdec5b276186297b89de4c353b99cb6813b91f936e6743b0dd1cc","source":{"kind":"arxiv","id":"1402.0300","version":2},"attestation_state":"computed","paper":{"title":"Virtual braids from a topological viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Bruno Aaron Cisneros de La Cruz (IMB)","submitted_at":"2014-02-03T07:52:05Z","abstract_excerpt":"Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility, stability and Reidemeister moves. We show that virtual braids are in a bijective correspondence with abstract braids. Finally we demonstrate that for any abstract braid, its representative of minimal genus is unique up to compatibility and Reidemeister moves. The genus of such a representative is thus an invariant for virtual braids. We also give a complete "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.0300","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-02-03T07:52:05Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"b0d35c50b94f5efc03dbd3afc637a8655d4a9d4189c08bff6122c74a99514a03","abstract_canon_sha256":"c664041b4ee5079d3bf7136fa964b6ce12e46b9ef926ecd999d5bb0fc786c2ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:44.643725Z","signature_b64":"zqzZLOccAsmgKp07+UxpjMg/T75d8MkqzkJJNAxBRlRONGWf54kPW7g5DkQTis1Vw5hOoI9ZrbLBEqAd56YZAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24cda5049b7bdec5b276186297b89de4c353b99cb6813b91f936e6743b0dd1cc","last_reissued_at":"2026-05-17T23:49:44.643206Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:44.643206Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Virtual braids from a topological viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Bruno Aaron Cisneros de La Cruz (IMB)","submitted_at":"2014-02-03T07:52:05Z","abstract_excerpt":"Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility, stability and Reidemeister moves. We show that virtual braids are in a bijective correspondence with abstract braids. Finally we demonstrate that for any abstract braid, its representative of minimal genus is unique up to compatibility and Reidemeister moves. The genus of such a representative is thus an invariant for virtual braids. We also give a complete "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0300","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.0300","created_at":"2026-05-17T23:49:44.643270+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0300v2","created_at":"2026-05-17T23:49:44.643270+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0300","created_at":"2026-05-17T23:49:44.643270+00:00"},{"alias_kind":"pith_short_12","alias_value":"ETG2KBE3PPPM","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"ETG2KBE3PPPMLMTW","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"ETG2KBE3","created_at":"2026-05-18T12:28:28.263976+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ETG2KBE3PPPMLMTWDBRJPOE54T","json":"https://pith.science/pith/ETG2KBE3PPPMLMTWDBRJPOE54T.json","graph_json":"https://pith.science/api/pith-number/ETG2KBE3PPPMLMTWDBRJPOE54T/graph.json","events_json":"https://pith.science/api/pith-number/ETG2KBE3PPPMLMTWDBRJPOE54T/events.json","paper":"https://pith.science/paper/ETG2KBE3"},"agent_actions":{"view_html":"https://pith.science/pith/ETG2KBE3PPPMLMTWDBRJPOE54T","download_json":"https://pith.science/pith/ETG2KBE3PPPMLMTWDBRJPOE54T.json","view_paper":"https://pith.science/paper/ETG2KBE3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0300&json=true","fetch_graph":"https://pith.science/api/pith-number/ETG2KBE3PPPMLMTWDBRJPOE54T/graph.json","fetch_events":"https://pith.science/api/pith-number/ETG2KBE3PPPMLMTWDBRJPOE54T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ETG2KBE3PPPMLMTWDBRJPOE54T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ETG2KBE3PPPMLMTWDBRJPOE54T/action/storage_attestation","attest_author":"https://pith.science/pith/ETG2KBE3PPPMLMTWDBRJPOE54T/action/author_attestation","sign_citation":"https://pith.science/pith/ETG2KBE3PPPMLMTWDBRJPOE54T/action/citation_signature","submit_replication":"https://pith.science/pith/ETG2KBE3PPPMLMTWDBRJPOE54T/action/replication_record"}},"created_at":"2026-05-17T23:49:44.643270+00:00","updated_at":"2026-05-17T23:49:44.643270+00:00"}