{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CJ7HDGWJYH5OXU5OWNYDRNHGJR","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":"436022910197eff743a1c33440b18668d94b311798a1b6426c63e2fd1903c545","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-21T14:51:15Z","title_canon_sha256":"49742a450691012f0751699d146737209b381080c588cdb8e0a0f1d45da6a045"},"schema_version":"1.0","source":{"id":"1604.06453","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06453","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06453v1","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06453","created_at":"2026-05-18T01:16:28Z"},{"alias_kind":"pith_short_12","alias_value":"CJ7HDGWJYH5O","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CJ7HDGWJYH5OXU5O","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CJ7HDGWJ","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:50e03bb42b1fe5c0eddafcb2c65da28b8be86c1802a272a79d07e3ccb4370292","target":"graph","created_at":"2026-05-18T01:16:28Z","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":"We prove that the first positive eigenvalue, normalized by the volume, of the sub-Laplacian associated with a strictly pseudoconvex pseudo-Hermitian structure $\\\\theta$ on the CR sphere S 2n+1 $\\subset$ C n+1 , achieves its maximum when $\\\\theta$ is the standard contact form.","authors_text":"Ahmad El Soufi (LMPT), Amine Aribi (LMPT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-21T14:51:15Z","title":"The first positive eigenvalue of the sub-laplacian on cr spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06453","kind":"arxiv","version":1},"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":"sha256:9f5cf40d18705eff1afbd643a49c3a503262c3fe25894a80e5856fe684149ac2","target":"record","created_at":"2026-05-18T01:16:28Z","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":"436022910197eff743a1c33440b18668d94b311798a1b6426c63e2fd1903c545","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-21T14:51:15Z","title_canon_sha256":"49742a450691012f0751699d146737209b381080c588cdb8e0a0f1d45da6a045"},"schema_version":"1.0","source":{"id":"1604.06453","kind":"arxiv","version":1}},"canonical_sha256":"127e719ac9c1faebd3aeb37038b4e64c5c759a4aabc795c5ea2f07b5871058a8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"127e719ac9c1faebd3aeb37038b4e64c5c759a4aabc795c5ea2f07b5871058a8","first_computed_at":"2026-05-18T01:16:28.989129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:28.989129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GwTdN7aV8Kalp3w0+RpJAxQ6fpOHFX/rzKx1Fyg6/BeAqDdfbLTriOG2DxzmVZ/TYfc0QzHHthesiYfj9OVBAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:28.989731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06453","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f5cf40d18705eff1afbd643a49c3a503262c3fe25894a80e5856fe684149ac2","sha256:50e03bb42b1fe5c0eddafcb2c65da28b8be86c1802a272a79d07e3ccb4370292"],"state_sha256":"f61d36afe186cf62d72dca06fa16082653d6907b6e57c76b2cd9c7828e8293e0"}