{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:XSN2N3I7CHUGPCPAZCGQ32G4SK","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":"1a5f1efbe276258dce934f2c74553b7c3fe53c722208114fba7677d1c26caeb2","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.GT","submitted_at":"2003-11-12T09:30:28Z","title_canon_sha256":"b2b86ca07418c3aa0e1420ea6c91509252805ef071d6ae3a90a228191f973445"},"schema_version":"1.0","source":{"id":"math/0311185","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0311185","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0311185v5","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0311185","created_at":"2026-05-18T01:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"XSN2N3I7CHUG","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XSN2N3I7CHUGPCPA","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XSN2N3I7","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:bac29a74d5a8fe468c15f76b82f607a78473d28afbc61a9601774ec134162047","target":"graph","created_at":"2026-05-18T01:05:28Z","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":"A virtual string is a scheme of self-intersections of a closed curve on a surface. We study algebraic invariants of strings as well as two equivalence relations on the set of strings: homotopy and cobordism. We show that the homotopy invariants of strings form an infinite dimensional Lie group.\n We also discuss connections between virtual strings and virtual knots.","authors_text":"Vladimir Turaev","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2003-11-12T09:30:28Z","title":"Virtual strings and their cobordisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0311185","kind":"arxiv","version":5},"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":"sha256:0b71fb0ea0e91cd22e3b828923e48b5c0197f461505b29e30f00018f6d4dd6a2","target":"record","created_at":"2026-05-18T01:05:28Z","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":"1a5f1efbe276258dce934f2c74553b7c3fe53c722208114fba7677d1c26caeb2","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.GT","submitted_at":"2003-11-12T09:30:28Z","title_canon_sha256":"b2b86ca07418c3aa0e1420ea6c91509252805ef071d6ae3a90a228191f973445"},"schema_version":"1.0","source":{"id":"math/0311185","kind":"arxiv","version":5}},"canonical_sha256":"bc9ba6ed1f11e86789e0c88d0de8dc9286ac4bf382061b59bc8d7b32e10b0a76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc9ba6ed1f11e86789e0c88d0de8dc9286ac4bf382061b59bc8d7b32e10b0a76","first_computed_at":"2026-05-18T01:05:28.527908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:28.527908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cf1FbwY+FKkEtoT5t7CxPqsGAR0BoV8OOefESwGTyeUzve2HiU7ABoJCAQnFNtElh8cftzGzNmOj61OuvJImAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:28.528481Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0311185","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b71fb0ea0e91cd22e3b828923e48b5c0197f461505b29e30f00018f6d4dd6a2","sha256:bac29a74d5a8fe468c15f76b82f607a78473d28afbc61a9601774ec134162047"],"state_sha256":"fb06f6ae4cfbaa2dc9f16847f84cf2e1925d7bc0bf9b8d0c04efd55254f4a51b"}