{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:M3GS7FQNZ2Z4BAGVMNJNPJIZGS","short_pith_number":"pith:M3GS7FQN","schema_version":"1.0","canonical_sha256":"66cd2f960dceb3c080d56352d7a51934af80393db3a8a109d17a7c5f95cc29cc","source":{"kind":"arxiv","id":"1211.4227","version":6},"attestation_state":"computed","paper":{"title":"Contact stationary Legendrian surfaces in $S^5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SG"],"primary_cat":"math.DG","authors_text":"Yong Luo","submitted_at":"2012-11-18T15:57:50Z","abstract_excerpt":"Let $(M^5,\\alpha,g_\\alpha,J)$ be a 5-dimensional Sasakian Einstein manifold with contact 1-form $\\alpha$, associated metric $g_\\alpha$ and almost complex structure $J$ and $L$ a contact stationary Legendrian surface in $M^5$. We will prove that $L$ satisfies the following equation\n  \\begin{eqnarray}\\label{equ}\n  -\\Delta^\\nu H+(K-1)H=0, \\end{eqnarray} where $\\Delta^\\nu$ is the normal Laplacian w.r.t the metric $g$ on $L$ induced from $g_\\alpha$ and $K$ is the Gauss curvature of $(L,g)$.\n  Using equation \\eqref{equ} and a new Simons' type inequality for Legendrian surfaces in the standard unit s"},"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":"1211.4227","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-18T15:57:50Z","cross_cats_sorted":["math.AP","math.SG"],"title_canon_sha256":"cdf8c2c0966100a2ca3ddab4fc61551aef8aff81f17aec9df59f33ec2fcad9f9","abstract_canon_sha256":"3793643474855832a5f141ccb76acbb3546a6c21c088cc8869c6044c0de407cd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:01.056292Z","signature_b64":"5so700XiG5BQyCH+0IGm0U++WBImOqj8p1w3aPDEIh3LLdIkALMg3b5631BgyGaPKVMtiC+3Kcx29i6iq3jqAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66cd2f960dceb3c080d56352d7a51934af80393db3a8a109d17a7c5f95cc29cc","last_reissued_at":"2026-05-18T00:21:01.055698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:01.055698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Contact stationary Legendrian surfaces in $S^5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.SG"],"primary_cat":"math.DG","authors_text":"Yong Luo","submitted_at":"2012-11-18T15:57:50Z","abstract_excerpt":"Let $(M^5,\\alpha,g_\\alpha,J)$ be a 5-dimensional Sasakian Einstein manifold with contact 1-form $\\alpha$, associated metric $g_\\alpha$ and almost complex structure $J$ and $L$ a contact stationary Legendrian surface in $M^5$. We will prove that $L$ satisfies the following equation\n  \\begin{eqnarray}\\label{equ}\n  -\\Delta^\\nu H+(K-1)H=0, \\end{eqnarray} where $\\Delta^\\nu$ is the normal Laplacian w.r.t the metric $g$ on $L$ induced from $g_\\alpha$ and $K$ is the Gauss curvature of $(L,g)$.\n  Using equation \\eqref{equ} and a new Simons' type inequality for Legendrian surfaces in the standard unit s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4227","kind":"arxiv","version":6},"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":"1211.4227","created_at":"2026-05-18T00:21:01.055783+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.4227v6","created_at":"2026-05-18T00:21:01.055783+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4227","created_at":"2026-05-18T00:21:01.055783+00:00"},{"alias_kind":"pith_short_12","alias_value":"M3GS7FQNZ2Z4","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"M3GS7FQNZ2Z4BAGV","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"M3GS7FQN","created_at":"2026-05-18T12:27:14.488303+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/M3GS7FQNZ2Z4BAGVMNJNPJIZGS","json":"https://pith.science/pith/M3GS7FQNZ2Z4BAGVMNJNPJIZGS.json","graph_json":"https://pith.science/api/pith-number/M3GS7FQNZ2Z4BAGVMNJNPJIZGS/graph.json","events_json":"https://pith.science/api/pith-number/M3GS7FQNZ2Z4BAGVMNJNPJIZGS/events.json","paper":"https://pith.science/paper/M3GS7FQN"},"agent_actions":{"view_html":"https://pith.science/pith/M3GS7FQNZ2Z4BAGVMNJNPJIZGS","download_json":"https://pith.science/pith/M3GS7FQNZ2Z4BAGVMNJNPJIZGS.json","view_paper":"https://pith.science/paper/M3GS7FQN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.4227&json=true","fetch_graph":"https://pith.science/api/pith-number/M3GS7FQNZ2Z4BAGVMNJNPJIZGS/graph.json","fetch_events":"https://pith.science/api/pith-number/M3GS7FQNZ2Z4BAGVMNJNPJIZGS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M3GS7FQNZ2Z4BAGVMNJNPJIZGS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M3GS7FQNZ2Z4BAGVMNJNPJIZGS/action/storage_attestation","attest_author":"https://pith.science/pith/M3GS7FQNZ2Z4BAGVMNJNPJIZGS/action/author_attestation","sign_citation":"https://pith.science/pith/M3GS7FQNZ2Z4BAGVMNJNPJIZGS/action/citation_signature","submit_replication":"https://pith.science/pith/M3GS7FQNZ2Z4BAGVMNJNPJIZGS/action/replication_record"}},"created_at":"2026-05-18T00:21:01.055783+00:00","updated_at":"2026-05-18T00:21:01.055783+00:00"}