{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:Q7PCURY77HCVZ6LABNLOXCQLDN","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":"ecd9ba00756b1d890711d1a7a466452771fc8a7c35695ab659c5ad1d4daae67c","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2002-01-22T23:32:45Z","title_canon_sha256":"c717aa8732e5ac5eeb1a2f96d5dff56d1aa267ebafa8f4ba29d5eb016d0f9b64"},"schema_version":"1.0","source":{"id":"math/0201219","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0201219","created_at":"2026-07-04T15:39:27Z"},{"alias_kind":"arxiv_version","alias_value":"math/0201219v2","created_at":"2026-07-04T15:39:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0201219","created_at":"2026-07-04T15:39:27Z"},{"alias_kind":"pith_short_12","alias_value":"Q7PCURY77HCV","created_at":"2026-07-04T15:39:27Z"},{"alias_kind":"pith_short_16","alias_value":"Q7PCURY77HCVZ6LA","created_at":"2026-07-04T15:39:27Z"},{"alias_kind":"pith_short_8","alias_value":"Q7PCURY7","created_at":"2026-07-04T15:39:27Z"}],"graph_snapshots":[{"event_id":"sha256:d847e43cfa4f16afb1c2a01f7fd70f6327207f8657cd1942dfe9cc4d2af19f32","target":"graph","created_at":"2026-07-04T15:39:27Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0201219/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article explains how to construct immersed Lagrangian submanifolds in C^2 that are asymptotic at large distance from the origin to a given braid in the 3-sphere. The self-intersections of the Lagrangians are related to the crossings of the braid. These Lagrangians are then used to construct immersed Lagrangians in the vector bundle O(-1) oplus O(-1) over the Riemann sphere which are asymptotic at large distance from the zero section to braids.","authors_text":"Clifford Henry Taubes","cross_cats":["math-ph","math.GT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2002-01-22T23:32:45Z","title":"Lagrangians for the Gopakumar-Vafa conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0201219","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:f8f4fd7a0c95ed107b1016afe720cea19d590694ecdae06c00d8dcc1fffdac03","target":"record","created_at":"2026-07-04T15:39:27Z","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":"ecd9ba00756b1d890711d1a7a466452771fc8a7c35695ab659c5ad1d4daae67c","cross_cats_sorted":["math-ph","math.GT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2002-01-22T23:32:45Z","title_canon_sha256":"c717aa8732e5ac5eeb1a2f96d5dff56d1aa267ebafa8f4ba29d5eb016d0f9b64"},"schema_version":"1.0","source":{"id":"math/0201219","kind":"arxiv","version":2}},"canonical_sha256":"87de2a471ff9c55cf9600b56eb8a0b1b78c9a046bbd60e8b8f8273a0c7ceaa91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87de2a471ff9c55cf9600b56eb8a0b1b78c9a046bbd60e8b8f8273a0c7ceaa91","first_computed_at":"2026-07-04T15:39:27.609436Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:39:27.609436Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3tDWMejRB/qw1fvqSxNGAV4WQIhR3jUz6LdIOv/pt+R0F+pQ8yJDtaqCnjUtjOPCMUcNo6OlcIN8mtpkc1liCg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:39:27.609854Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0201219","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8f4fd7a0c95ed107b1016afe720cea19d590694ecdae06c00d8dcc1fffdac03","sha256:d847e43cfa4f16afb1c2a01f7fd70f6327207f8657cd1942dfe9cc4d2af19f32"],"state_sha256":"e950d9b7b1286b0468df8c05fab9375aa01e95763dd796e7944e162bc492922a"}