{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:F5MZF75FYBP7ZEGC3XSP54OSLL","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":"f99609c4071dd038a774d66f471326d38fa5675f03025fc318df38f477e2b313","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-11T09:26:46Z","title_canon_sha256":"7c680295cbbe0483f661ac18ef86fd2637e4bc5d21e8e08a62e347e829e37dde"},"schema_version":"1.0","source":{"id":"1104.1889","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1889","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1889v1","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1889","created_at":"2026-05-18T04:24:36Z"},{"alias_kind":"pith_short_12","alias_value":"F5MZF75FYBP7","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"F5MZF75FYBP7ZEGC","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"F5MZF75F","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:6df3ebdfc5d11a8f8c3dda7cee856950b52fdfc146baf7dec4105efd5c5e8d5a","target":"graph","created_at":"2026-05-18T04:24:36Z","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 show that the scalar curvature of a steady gradient Ricci soliton satisfying that the ratio between the square norm of the Ricci tensor and the square of the scalar curvature is bounded by one half, is boundend from below by the hyperbolic secant of one half the distance function from a fixed point.","authors_text":"Eduardo Garcia-Rio, Manuel Fernandez-Lopez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-11T09:26:46Z","title":"A sharp lower bound for the scalar curvature of certain steady gradient Ricci solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1889","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:dc02d168bb7d00224555b0c15716070f04b757b96082df78aac9d543c2a855d5","target":"record","created_at":"2026-05-18T04:24:36Z","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":"f99609c4071dd038a774d66f471326d38fa5675f03025fc318df38f477e2b313","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-11T09:26:46Z","title_canon_sha256":"7c680295cbbe0483f661ac18ef86fd2637e4bc5d21e8e08a62e347e829e37dde"},"schema_version":"1.0","source":{"id":"1104.1889","kind":"arxiv","version":1}},"canonical_sha256":"2f5992ffa5c05ffc90c2dde4fef1d25adeb3c8989970ddf023424cd4511a610c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f5992ffa5c05ffc90c2dde4fef1d25adeb3c8989970ddf023424cd4511a610c","first_computed_at":"2026-05-18T04:24:36.912068Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:36.912068Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"78QF0Xlq/mZtcEcRhuvrwlKW0X9Qc4qT/TNWF2EnQJB7QrAqxInMuzetZLT0GXQzVmRU39LbrBzBew9avxMhCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:36.912458Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1889","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc02d168bb7d00224555b0c15716070f04b757b96082df78aac9d543c2a855d5","sha256:6df3ebdfc5d11a8f8c3dda7cee856950b52fdfc146baf7dec4105efd5c5e8d5a"],"state_sha256":"11ac70b7ff096689a0634045cac1e42bba8fa26d89167a6fb013a684ea523647"}