{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Q5LTH3SMV3U66T7DCBBL4P4XRH","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":"4d5e49693f4122ed7f84d4a1dbb9f444d08ce413c8f18ba78afcd14433571080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-07T15:23:04Z","title_canon_sha256":"2e478a0641e94f4ea6fa393f01fa9fd81eae308f37b749a1a5130c6ff4cf80d4"},"schema_version":"1.0","source":{"id":"1408.1621","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1621","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1621v1","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1621","created_at":"2026-05-18T02:45:40Z"},{"alias_kind":"pith_short_12","alias_value":"Q5LTH3SMV3U6","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"Q5LTH3SMV3U66T7D","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"Q5LTH3SM","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:ce1e57cd8bb99f4d7c4b8c58c4d7e1a9affdaa0201c493f042a9382a9c1b32ea","target":"graph","created_at":"2026-05-18T02:45:40Z","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":"The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the approach of quasi-Einstein manifolds which is directly related to Einstein warped product. In particular, we present an obstruction for the existence of such a class of manifolds.","authors_text":"A. Barros, E. Ribeiro Jr, R. Batista","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-07T15:23:04Z","title":"Bounds on volume growth of geodesic balls for Einstein warped products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1621","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:bfd594b2fd807a040856c5e8bef28d1be363644645a757e3b93c7111767b8c91","target":"record","created_at":"2026-05-18T02:45:40Z","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":"4d5e49693f4122ed7f84d4a1dbb9f444d08ce413c8f18ba78afcd14433571080","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-08-07T15:23:04Z","title_canon_sha256":"2e478a0641e94f4ea6fa393f01fa9fd81eae308f37b749a1a5130c6ff4cf80d4"},"schema_version":"1.0","source":{"id":"1408.1621","kind":"arxiv","version":1}},"canonical_sha256":"875733ee4caee9ef4fe31042be3f9789f70fc5b01acd46daae578c2a0b5474aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"875733ee4caee9ef4fe31042be3f9789f70fc5b01acd46daae578c2a0b5474aa","first_computed_at":"2026-05-18T02:45:40.048898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:40.048898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pdQru46MSdNbYz8Gp66osVVcgH54HVokJ3NIYyh+fs+ZuY1SMfLAnP5QY8JJe4QOuJshHg/E1TILvI0a4GAICQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:40.049427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1621","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfd594b2fd807a040856c5e8bef28d1be363644645a757e3b93c7111767b8c91","sha256:ce1e57cd8bb99f4d7c4b8c58c4d7e1a9affdaa0201c493f042a9382a9c1b32ea"],"state_sha256":"951c359216a9bb0be0eb7c4ecae46816aa34126d8d2947d16a03b9efdef2b735"}