{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MBLD3QA5UNVHPBT5RQR7DNBNVW","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":"af1a82264cb1f44fa26513bdbeb97055661c5e69477f1dd52ec4eefa8e58a499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-18T08:45:24Z","title_canon_sha256":"939b41bf600ee7b3e411c1ac44dd30a72a14bb12a6feb916663d3a69aaa65183"},"schema_version":"1.0","source":{"id":"1003.3527","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1003.3527","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1003.3527v2","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.3527","created_at":"2026-05-18T04:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"MBLD3QA5UNVH","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MBLD3QA5UNVHPBT5","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MBLD3QA5","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:5e501ed9d53d8f0854ea5861d80a3baa661b050fefba0cd869a0fc3301c0f2e1","target":"graph","created_at":"2026-05-18T04:22:40Z","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":"Schur's lemma states that every Einstein manifold of dimension $n\\geq 3$ has constant scalar curvature. Here $(M,g)$ is defined to be Einstein if its traceless Ricci tensor $$\\Rico:=\\Ric-\\frac{R}{n}g$$ is identically zero. In this short note we ask to what extent the scalar curvature is constant if the traceless Ricci tensor is assumed to be \\emph{small} rather than identically zero.","authors_text":"Camillo De Lellis, Peter M. Topping","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-18T08:45:24Z","title":"Almost-Schur lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3527","kind":"arxiv","version":2},"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:d7196cab6f2fdc7a099439e447bc6dab85a841b8ecdf8dd6d2251e11c1725e20","target":"record","created_at":"2026-05-18T04:22:40Z","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":"af1a82264cb1f44fa26513bdbeb97055661c5e69477f1dd52ec4eefa8e58a499","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-03-18T08:45:24Z","title_canon_sha256":"939b41bf600ee7b3e411c1ac44dd30a72a14bb12a6feb916663d3a69aaa65183"},"schema_version":"1.0","source":{"id":"1003.3527","kind":"arxiv","version":2}},"canonical_sha256":"60563dc01da36a77867d8c23f1b42dadad4ac9c768f80b188760776927b65856","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60563dc01da36a77867d8c23f1b42dadad4ac9c768f80b188760776927b65856","first_computed_at":"2026-05-18T04:22:40.420308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:40.420308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9tDocq3pz+RJK4PiEdcEWvJrwHk2/buzmPKJhgvYRsq0q506e00XZfjHZkCndWEr1C7ERPhZ+/D+mQZL86SCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:40.420690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1003.3527","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7196cab6f2fdc7a099439e447bc6dab85a841b8ecdf8dd6d2251e11c1725e20","sha256:5e501ed9d53d8f0854ea5861d80a3baa661b050fefba0cd869a0fc3301c0f2e1"],"state_sha256":"1360ce542af1f507b0af6377ff09404e69f49a64725ebe339691e14e0f32e38d"}