{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FRD5XQMUQVDWXWBUYOT6F76EDJ","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":"44a957c483d250f3c1577c8b90d8a484378391a3612ff554295e1096e3a2236a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-10T21:28:08Z","title_canon_sha256":"45cbe21a357e4d7f16bd0b3d5167e56b46b32924bd005a1e7f8ee110ce5002d6"},"schema_version":"1.0","source":{"id":"1505.02440","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02440","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02440v2","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02440","created_at":"2026-05-18T01:21:23Z"},{"alias_kind":"pith_short_12","alias_value":"FRD5XQMUQVDW","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"FRD5XQMUQVDWXWBU","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"FRD5XQMU","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:291ae3369b54def847d65544c65355d81cdc25787158d5b69ede654a7c75040e","target":"graph","created_at":"2026-05-18T01:21:23Z","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":"In 2003, Del Pino and Dolbeault [14] and Gentil [19] investigated, independently, best constants and extremals associated to Euclidean Lp-entropy inequalities for p > 1. In this work, we present some contributions in the Riemannian context. Namely, let (M,g) be a closed Riemannian manifold of dimension n >= 3. For 1 < p <= 2, we establish the validity of the sharp Riemannian Lp-entropy inequality\n  int_M |u|^p log(|u|^p) dv_g <= n/p log ( A_{opt} int_M |Grad_g u|^p dv_g + B )\n  on all functions u em H^{1,p}(M) such that ||u||_{Lp(M)} = 1 for some constant B. Moreover, we prove that the first b","authors_text":"Jurandir Ceccon, Marcos Montenegro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-10T21:28:08Z","title":"Sharp Lp-entropy inequalities on manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02440","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":"sha256:8e3dd8fdeeea3d54ea65eb5c73212250af11db5e3ed2278190de00c5aa7db1e6","target":"record","created_at":"2026-05-18T01:21:23Z","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":"44a957c483d250f3c1577c8b90d8a484378391a3612ff554295e1096e3a2236a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-05-10T21:28:08Z","title_canon_sha256":"45cbe21a357e4d7f16bd0b3d5167e56b46b32924bd005a1e7f8ee110ce5002d6"},"schema_version":"1.0","source":{"id":"1505.02440","kind":"arxiv","version":2}},"canonical_sha256":"2c47dbc19485476bd834c3a7e2ffc41a5ba5cfaf018587242787ff5dd2981669","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c47dbc19485476bd834c3a7e2ffc41a5ba5cfaf018587242787ff5dd2981669","first_computed_at":"2026-05-18T01:21:23.081199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:23.081199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0edHIiKTf52hcQJdKhSUqDbVawqHei1yF4H+BTJ0YaXiRHqI9xUDY84vp/7QOaKBHGtKgCyaxgnrjOyndNwxDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:23.081807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02440","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e3dd8fdeeea3d54ea65eb5c73212250af11db5e3ed2278190de00c5aa7db1e6","sha256:291ae3369b54def847d65544c65355d81cdc25787158d5b69ede654a7c75040e"],"state_sha256":"b80c42b247ae90cefe59ddb56396127ff33ba8eafcd3eb07f7286af6efee60f4"}