{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SEZPCSEHOYT44XYKWOXUX7VWSM","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":"143093ad8131c5bf87ada98b195904c948b68f34df82c09de5b7a1f8e508565d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-20T09:06:31Z","title_canon_sha256":"7196028d427c41855bcf8288ba1f4cc97d9b18db2235adc4173f869313aaaba3"},"schema_version":"1.0","source":{"id":"1103.3838","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3838","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3838v1","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3838","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"SEZPCSEHOYT4","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SEZPCSEHOYT44XYK","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SEZPCSEH","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:5bffb891ca46234300a037f353754ca31a862d12873f9c5f44edb12ff4ab4435","target":"graph","created_at":"2026-05-18T04:26:22Z","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":"By improving the analysis developed in the study of $\\s_k$-Yamabe problem, we prove in this paper that the De Lellis-Topping inequality is true on 3-dimensional Riemannian manifolds of nonnegative scalar curvature. More precisely, if $(M^3, g)$ is a 3-dimensional closed Riemannian manifold with non-negative scalar curvature, then \\[\\int_M |Ric-\\frac{\\bar R} 3 g|^2 dv (g)\\le 9\\int_M |Ric-\\frac{R} 3 g|^2dv(g), \\] where $\\bar R=vol (g)^{-1} \\int_M R dv(g)$ is the average of the scalar curvature $R$ of $g$. Equality holds if and only if $(M^3,g)$ is a space form. We in fact study the following new","authors_text":"Guofang Wang, Yuxin Ge","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-20T09:06:31Z","title":"A new conformal invariant on 3-dimensional manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3838","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:dcea4f26a2d0908ad16f84d63415cdd2c6f409137306f6253c32e76567bd190c","target":"record","created_at":"2026-05-18T04:26:22Z","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":"143093ad8131c5bf87ada98b195904c948b68f34df82c09de5b7a1f8e508565d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-20T09:06:31Z","title_canon_sha256":"7196028d427c41855bcf8288ba1f4cc97d9b18db2235adc4173f869313aaaba3"},"schema_version":"1.0","source":{"id":"1103.3838","kind":"arxiv","version":1}},"canonical_sha256":"9132f148877627ce5f0ab3af4bfeb6932b177c367ac92e1855e4f093e3a276a9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9132f148877627ce5f0ab3af4bfeb6932b177c367ac92e1855e4f093e3a276a9","first_computed_at":"2026-05-18T04:26:22.225677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:22.225677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Md+7bdU47xZLd+JkW6XOQ1bnJ6mqSTxf5vifFMMNvnYhigw4h4MXV5EkWdefPGhAfXji+rWd7j7sDWuJzQGjDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:22.226114Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3838","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dcea4f26a2d0908ad16f84d63415cdd2c6f409137306f6253c32e76567bd190c","sha256:5bffb891ca46234300a037f353754ca31a862d12873f9c5f44edb12ff4ab4435"],"state_sha256":"40e0b8eb6363425c20d160b279efc8fcd7221f78e120752e17174e7a30badcef"}