{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HVIGWW5YDP7W7ZUWBI5S5BTO3C","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":"990e0edda71b1d7d7312d5e517d889a029d3bbdd77db9e33400819064d295d26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-09T16:44:28Z","title_canon_sha256":"3658d75a512e2ff48eac1292842f2532ac571629391054990ccb0db919a28a72"},"schema_version":"1.0","source":{"id":"1304.2658","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2658","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2658v6","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2658","created_at":"2026-05-18T02:38:17Z"},{"alias_kind":"pith_short_12","alias_value":"HVIGWW5YDP7W","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HVIGWW5YDP7W7ZUW","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HVIGWW5Y","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:19a47b938a49c1ca875e2907e283b7a26db3ecf651639a8ee8f9ac6d2f37cb22","target":"graph","created_at":"2026-05-18T02:38:17Z","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":"Measure contraction properties are generalizations of the notion of Ricci curvature lower bounds in Riemannian geometry to more general metric measure spaces. In this paper, we give sufficient conditions for a Sasakian manifold equipped with a natural sub-Riemannian distance to satisfy these properties. Moreover, the sufficient conditions are defined by the Tanaka-Webster curvature. This generalizes the earlier work in \\cite{AgLe1} for the three dimensional case and in \\cite{Ju} for the Heisenberg group. To obtain our results we use the intrinsic Jacobi equations along sub-Riemannian extremals","authors_text":"Chengbo Li, Igor zelenko, Paul W. Y. Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-09T16:44:28Z","title":"Ricci curvature type lower bounds for sub-Riemannian structures on Sasakian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2658","kind":"arxiv","version":6},"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":"sha256:1da479dca6b8b4d31608945241dc1645f3d04c6af7cc3f03a22c1b98ef26a7c5","target":"record","created_at":"2026-05-18T02:38:17Z","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":"990e0edda71b1d7d7312d5e517d889a029d3bbdd77db9e33400819064d295d26","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-09T16:44:28Z","title_canon_sha256":"3658d75a512e2ff48eac1292842f2532ac571629391054990ccb0db919a28a72"},"schema_version":"1.0","source":{"id":"1304.2658","kind":"arxiv","version":6}},"canonical_sha256":"3d506b5bb81bff6fe6960a3b2e866ed8baafd2c47f9b40def951449b1166ccf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d506b5bb81bff6fe6960a3b2e866ed8baafd2c47f9b40def951449b1166ccf9","first_computed_at":"2026-05-18T02:38:17.256902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:17.256902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pU+PvDeewLdh+9bwJsqze3POKsPp4F+3L09B4Eme5OZbGCMT5+rWNEppODhSCCFq5keVqBwx6RxSsnfcA5frBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:17.257636Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2658","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1da479dca6b8b4d31608945241dc1645f3d04c6af7cc3f03a22c1b98ef26a7c5","sha256:19a47b938a49c1ca875e2907e283b7a26db3ecf651639a8ee8f9ac6d2f37cb22"],"state_sha256":"b8d4482901e2e99210663b629bd94207d52ed57807522b0db307bdd8048ab16e"}