{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:C4ROSHAXG2DJ7Y7Y2LEUGH6YGE","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":"f992a348a96f1f278248e3e94ab62011c010976e8d761cd87345d1af9bf01a1b","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-17T15:39:11Z","title_canon_sha256":"1687e90b50495d05a3011aa8958cf089ca963986467a6a9469561695f6aae678"},"schema_version":"1.0","source":{"id":"1207.4033","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4033","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4033v3","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4033","created_at":"2026-05-18T03:15:57Z"},{"alias_kind":"pith_short_12","alias_value":"C4ROSHAXG2DJ","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"C4ROSHAXG2DJ7Y7Y","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"C4ROSHAX","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:fb20efb027a961963b09fc6d56ed42d44bc313d19e2a12d41af8bce870190a24","target":"graph","created_at":"2026-05-18T03:15:57Z","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":"We discuss a sharp lower bound for the first positive eigenvalue of the sublaplacian on a closed, strictly pseudoconvex pseudo-hermitian manifold of dimension $2m+1\\geq 5$. We prove that the equality holds iff the manifold is equivalent to the CR sphere up to a scaling. The essential step is a characterization of the CR sphere when there is a nonzero function satisfying a certain overdetermined system.","authors_text":"Song-Ying Li, Xiaodong Wang","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-17T15:39:11Z","title":"An Obata-type Theorem in CR Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4033","kind":"arxiv","version":3},"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:e7a72bc855d20c8ae3dc249c02961644572451187747cc8394a484254c7613a3","target":"record","created_at":"2026-05-18T03:15:57Z","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":"f992a348a96f1f278248e3e94ab62011c010976e8d761cd87345d1af9bf01a1b","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-17T15:39:11Z","title_canon_sha256":"1687e90b50495d05a3011aa8958cf089ca963986467a6a9469561695f6aae678"},"schema_version":"1.0","source":{"id":"1207.4033","kind":"arxiv","version":3}},"canonical_sha256":"1722e91c1736869fe3f8d2c9431fd83106f8ed82c24529123c0bc62b8ad962a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1722e91c1736869fe3f8d2c9431fd83106f8ed82c24529123c0bc62b8ad962a5","first_computed_at":"2026-05-18T03:15:57.767432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:57.767432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NqU321ggd10156fzOcRsA8p1XVbxpoXwJYJNhNiFCcaUx468GrILGqioY2MPwui7IG42RjQkxKso0yVqreOmCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:57.767946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4033","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7a72bc855d20c8ae3dc249c02961644572451187747cc8394a484254c7613a3","sha256:fb20efb027a961963b09fc6d56ed42d44bc313d19e2a12d41af8bce870190a24"],"state_sha256":"751c259b6a04d8665aa0a3aa2f663578c8666b0c478cd4ed62ef64d8423d03a3"}