{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:ZP5LSOHIQJVVST7XOXNXD4JE6U","short_pith_number":"pith:ZP5LSOHI","schema_version":"1.0","canonical_sha256":"cbfab938e8826b594ff775db71f124f52e166cee7a0a7288c49ba1f8f504f7dc","source":{"kind":"arxiv","id":"1406.0875","version":2},"attestation_state":"computed","paper":{"title":"Virtual Legendrian Isotopy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"R. Sadykov, V. Chernov","submitted_at":"2014-06-03T20:59:41Z","abstract_excerpt":"An elementary stabilization of a Legendrian link $L$ in the spherical cotangent bundle $ST^*M$ of a surface $M$ is a surgery that results in attaching a handle to $M$ along two discs away from the image in $M$ of the projection of the link $L$. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies.\n  In contrast to Legendrian knots, virtual Legendrian knots enjoy the property that there is a bijective correspondence between the virtual Legendrian knots and the equivalence classes of Gauss diagrams.\n  We study virtual Legendrian isotopy class"},"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":"1406.0875","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-06-03T20:59:41Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"7084117467a67ada08052ce7be8580756435a2b7e258e3a2bf46307c4222a285","abstract_canon_sha256":"de26d4b862dc124a645448f56dfafc819b9e2b374810f81e49c1596e7d07097d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:48.138434Z","signature_b64":"MqI1Ns7rtXQaOkaTKDSeaODCPiDSP93bMY4BD2n6CRDQRA/QGgidEqi+zcKix+iKtimFl29l9ynDNtR6JPePCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cbfab938e8826b594ff775db71f124f52e166cee7a0a7288c49ba1f8f504f7dc","last_reissued_at":"2026-05-18T02:39:48.137932Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:48.137932Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Virtual Legendrian Isotopy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"R. Sadykov, V. Chernov","submitted_at":"2014-06-03T20:59:41Z","abstract_excerpt":"An elementary stabilization of a Legendrian link $L$ in the spherical cotangent bundle $ST^*M$ of a surface $M$ is a surgery that results in attaching a handle to $M$ along two discs away from the image in $M$ of the projection of the link $L$. A virtual Legendrian isotopy is a composition of stabilizations, destabilizations and Legendrian isotopies.\n  In contrast to Legendrian knots, virtual Legendrian knots enjoy the property that there is a bijective correspondence between the virtual Legendrian knots and the equivalence classes of Gauss diagrams.\n  We study virtual Legendrian isotopy class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0875","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":"1406.0875","created_at":"2026-05-18T02:39:48.138005+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.0875v2","created_at":"2026-05-18T02:39:48.138005+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0875","created_at":"2026-05-18T02:39:48.138005+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZP5LSOHIQJVV","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZP5LSOHIQJVVST7X","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZP5LSOHI","created_at":"2026-05-18T12:28:59.999130+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/ZP5LSOHIQJVVST7XOXNXD4JE6U","json":"https://pith.science/pith/ZP5LSOHIQJVVST7XOXNXD4JE6U.json","graph_json":"https://pith.science/api/pith-number/ZP5LSOHIQJVVST7XOXNXD4JE6U/graph.json","events_json":"https://pith.science/api/pith-number/ZP5LSOHIQJVVST7XOXNXD4JE6U/events.json","paper":"https://pith.science/paper/ZP5LSOHI"},"agent_actions":{"view_html":"https://pith.science/pith/ZP5LSOHIQJVVST7XOXNXD4JE6U","download_json":"https://pith.science/pith/ZP5LSOHIQJVVST7XOXNXD4JE6U.json","view_paper":"https://pith.science/paper/ZP5LSOHI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.0875&json=true","fetch_graph":"https://pith.science/api/pith-number/ZP5LSOHIQJVVST7XOXNXD4JE6U/graph.json","fetch_events":"https://pith.science/api/pith-number/ZP5LSOHIQJVVST7XOXNXD4JE6U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZP5LSOHIQJVVST7XOXNXD4JE6U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZP5LSOHIQJVVST7XOXNXD4JE6U/action/storage_attestation","attest_author":"https://pith.science/pith/ZP5LSOHIQJVVST7XOXNXD4JE6U/action/author_attestation","sign_citation":"https://pith.science/pith/ZP5LSOHIQJVVST7XOXNXD4JE6U/action/citation_signature","submit_replication":"https://pith.science/pith/ZP5LSOHIQJVVST7XOXNXD4JE6U/action/replication_record"}},"created_at":"2026-05-18T02:39:48.138005+00:00","updated_at":"2026-05-18T02:39:48.138005+00:00"}