{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GQJPHBAM3S5GNALNLIFINJE2CU","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":"deed4258b99802ea69bfd42fc1a14f1238c272b2a4668d05f0a632b5e764167e","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-25T15:37:07Z","title_canon_sha256":"79ebb8ec461708638c106049d35a744965604c95dd09a87f059991c59cc6c744"},"schema_version":"1.0","source":{"id":"1804.09632","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09632","created_at":"2026-05-18T00:17:31Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09632v1","created_at":"2026-05-18T00:17:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09632","created_at":"2026-05-18T00:17:31Z"},{"alias_kind":"pith_short_12","alias_value":"GQJPHBAM3S5G","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GQJPHBAM3S5GNALN","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GQJPHBAM","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:5433505ec3925e6b619ff2169122a8f6d4e018b0b38977e426e4a0479b66b24d","target":"graph","created_at":"2026-05-18T00:17:31Z","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 on the sphere $\\mathbb{S}^2$ the Lieb--Thirring inequalities for orthonormal families of scalar and vector functions both on the whole sphere and on proper domains on $\\mathbb{S}^2$. By way of applications we obtain an explicit estimate for the dimension of the attractor of the Navier--Stokes system on a domain on the sphere with Dirichlet non-slip boundary conditions.","authors_text":"Alexei Ilyin, Ari Laptev","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-25T15:37:07Z","title":"Lieb--Thirring inequalities on the sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09632","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:e97e087d3adb58471972ed8df2f1bd9dd04c844cf320a1ed7ccf93583eca26f0","target":"record","created_at":"2026-05-18T00:17:31Z","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":"deed4258b99802ea69bfd42fc1a14f1238c272b2a4668d05f0a632b5e764167e","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-04-25T15:37:07Z","title_canon_sha256":"79ebb8ec461708638c106049d35a744965604c95dd09a87f059991c59cc6c744"},"schema_version":"1.0","source":{"id":"1804.09632","kind":"arxiv","version":1}},"canonical_sha256":"3412f3840cdcba66816d5a0a86a49a15375a993e9a2dea65b10a27c98f0f5b01","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3412f3840cdcba66816d5a0a86a49a15375a993e9a2dea65b10a27c98f0f5b01","first_computed_at":"2026-05-18T00:17:31.195674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:31.195674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+naspx1bFjZaAsfxdKCDcwIw67PNd52l+6uUEohme0uF4xrzviVVd2Vg6GtU3chX0Jb/WwGO2onnmcSzA6R+DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:31.196467Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09632","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e97e087d3adb58471972ed8df2f1bd9dd04c844cf320a1ed7ccf93583eca26f0","sha256:5433505ec3925e6b619ff2169122a8f6d4e018b0b38977e426e4a0479b66b24d"],"state_sha256":"c84ecc357c398516998b121b7b9badb8d480641a252b78bb7a0f915364993a55"}