{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:JGPV5YAN5TSPUD72IUEKKBLFJS","short_pith_number":"pith:JGPV5YAN","schema_version":"1.0","canonical_sha256":"499f5ee00dece4fa0ffa4508a505654c943d9b9b09d351d24c2d48df2a01b231","source":{"kind":"arxiv","id":"1406.6316","version":1},"attestation_state":"computed","paper":{"title":"The space of compact self-shrinking solutions to the Lagrangian Mean Curvature Flow in $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jingyi Chen, John Man Shun Ma","submitted_at":"2014-06-24T17:19:33Z","abstract_excerpt":"Let $F_n :(\\Sigma, h_n) \\to \\mathbb C^2$ be a sequence of conformally immersed Lagrangian self-shrinkers with a uniform area upper bound to the mean curvature flow, and suppose that the sequence of metrics $\\{h_n\\}$ converges smoothly to a Riemannian metric $h$. We show that a subsequence of $\\{F_n\\}$ converges smoothly to a branched conformally immersed Lagrangian self-shrinker $F_\\infty : (\\Sigma, h)\\to \\mathbb C^2$. When the area bound is less than $16\\pi$, the limit $F_\\infty$ is an embedded torus. When the genus of $\\Sigma$ is one, we can drop the assumption on convergence $h_n\\to h$. Whe"},"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":"1406.6316","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-06-24T17:19:33Z","cross_cats_sorted":[],"title_canon_sha256":"7fe7fa372c3b45ef9ca886e0dfbf9676b24c0702868eab705d19594300a57cc9","abstract_canon_sha256":"559d6338e1798eaa3b521ae2b9be4be313af83ce89e25c15b2c633c06e7d616f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:31.449890Z","signature_b64":"SKRxnEFMaM2myoKhIhsOsGlnHJ4Enj/gXIyc95ZGFYbLk/abIK1Cca4lJTeKykhUDuXWycNVJELCzv8lBo24DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"499f5ee00dece4fa0ffa4508a505654c943d9b9b09d351d24c2d48df2a01b231","last_reissued_at":"2026-05-17T23:46:31.449274Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:31.449274Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The space of compact self-shrinking solutions to the Lagrangian Mean Curvature Flow in $\\mathbb C^2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jingyi Chen, John Man Shun Ma","submitted_at":"2014-06-24T17:19:33Z","abstract_excerpt":"Let $F_n :(\\Sigma, h_n) \\to \\mathbb C^2$ be a sequence of conformally immersed Lagrangian self-shrinkers with a uniform area upper bound to the mean curvature flow, and suppose that the sequence of metrics $\\{h_n\\}$ converges smoothly to a Riemannian metric $h$. We show that a subsequence of $\\{F_n\\}$ converges smoothly to a branched conformally immersed Lagrangian self-shrinker $F_\\infty : (\\Sigma, h)\\to \\mathbb C^2$. When the area bound is less than $16\\pi$, the limit $F_\\infty$ is an embedded torus. When the genus of $\\Sigma$ is one, we can drop the assumption on convergence $h_n\\to h$. Whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6316","kind":"arxiv","version":1},"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":"1406.6316","created_at":"2026-05-17T23:46:31.449385+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.6316v1","created_at":"2026-05-17T23:46:31.449385+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6316","created_at":"2026-05-17T23:46:31.449385+00:00"},{"alias_kind":"pith_short_12","alias_value":"JGPV5YAN5TSP","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_16","alias_value":"JGPV5YAN5TSPUD72","created_at":"2026-05-18T12:28:33.132498+00:00"},{"alias_kind":"pith_short_8","alias_value":"JGPV5YAN","created_at":"2026-05-18T12:28:33.132498+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/JGPV5YAN5TSPUD72IUEKKBLFJS","json":"https://pith.science/pith/JGPV5YAN5TSPUD72IUEKKBLFJS.json","graph_json":"https://pith.science/api/pith-number/JGPV5YAN5TSPUD72IUEKKBLFJS/graph.json","events_json":"https://pith.science/api/pith-number/JGPV5YAN5TSPUD72IUEKKBLFJS/events.json","paper":"https://pith.science/paper/JGPV5YAN"},"agent_actions":{"view_html":"https://pith.science/pith/JGPV5YAN5TSPUD72IUEKKBLFJS","download_json":"https://pith.science/pith/JGPV5YAN5TSPUD72IUEKKBLFJS.json","view_paper":"https://pith.science/paper/JGPV5YAN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.6316&json=true","fetch_graph":"https://pith.science/api/pith-number/JGPV5YAN5TSPUD72IUEKKBLFJS/graph.json","fetch_events":"https://pith.science/api/pith-number/JGPV5YAN5TSPUD72IUEKKBLFJS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JGPV5YAN5TSPUD72IUEKKBLFJS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JGPV5YAN5TSPUD72IUEKKBLFJS/action/storage_attestation","attest_author":"https://pith.science/pith/JGPV5YAN5TSPUD72IUEKKBLFJS/action/author_attestation","sign_citation":"https://pith.science/pith/JGPV5YAN5TSPUD72IUEKKBLFJS/action/citation_signature","submit_replication":"https://pith.science/pith/JGPV5YAN5TSPUD72IUEKKBLFJS/action/replication_record"}},"created_at":"2026-05-17T23:46:31.449385+00:00","updated_at":"2026-05-17T23:46:31.449385+00:00"}