{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2PL5QABOOAIERZGY3VAYB62WU2","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":"5d8f70a2515ccb7e69773408ee7013336de793206ef3f56bc02b4c32b34c8ce0","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-08T15:26:43Z","title_canon_sha256":"237c59462b33b1dc52906bcb41b219ad47a6e1ba341f71366c65642a0640fe30"},"schema_version":"1.0","source":{"id":"1505.02061","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02061","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02061v2","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02061","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"2PL5QABOOAIE","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2PL5QABOOAIERZGY","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2PL5QABO","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:9a29bfd81c92105868cee203b1c4ae832b1ed8d79764a60d248b3bccfe113440","target":"graph","created_at":"2026-05-17T23:46:55Z","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":"For metric measure spaces verifying the reduced curvature-dimension condition $CD^*(K,N)$ we prove a series of sharp functional inequalities under the additional assumption of essentially non-branching. Examples of spaces entering this framework are (weighted) Riemannian manifolds satisfying lower Ricci curvature bounds and their measured Gromov Hausdorff limits, Alexandrov spaces satisfying lower curvature bounds and more generally $RCD^*(K,N)$-spaces, Finsler manifolds endowed with a strongly convex norm and satisfying lower Ricci curvature bounds, etc.\n  In particular we prove Brunn-Minkows","authors_text":"Andrea Mondino, Fabio Cavalletti","cross_cats":["math.AP","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-08T15:26:43Z","title":"Sharp geometric and functional inequalities in metric measure spaces with lower Ricci curvature bounds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02061","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":"sha256:12db1ba03731b2a0e58c767a5d5fd87aa2dea55e53c618a978b126375328d543","target":"record","created_at":"2026-05-17T23:46:55Z","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":"5d8f70a2515ccb7e69773408ee7013336de793206ef3f56bc02b4c32b34c8ce0","cross_cats_sorted":["math.AP","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-05-08T15:26:43Z","title_canon_sha256":"237c59462b33b1dc52906bcb41b219ad47a6e1ba341f71366c65642a0640fe30"},"schema_version":"1.0","source":{"id":"1505.02061","kind":"arxiv","version":2}},"canonical_sha256":"d3d7d8002e701048e4d8dd4180fb56a692305e61a659c393204eca71b942f148","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d3d7d8002e701048e4d8dd4180fb56a692305e61a659c393204eca71b942f148","first_computed_at":"2026-05-17T23:46:55.962239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:55.962239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q1OEEWqCkG6EwE/h/QGjK3Q2P0XuBHTvqyfrIaSVuzoSwY8cWxa7Ev2l9MKqx7OCf+fH1sbJ3U+Vivab8vwRDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:55.962960Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02061","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12db1ba03731b2a0e58c767a5d5fd87aa2dea55e53c618a978b126375328d543","sha256:9a29bfd81c92105868cee203b1c4ae832b1ed8d79764a60d248b3bccfe113440"],"state_sha256":"c400a7261420cb0cd359d71c62a1b7fdea5f530ce7d41e623d5096ec86a25042"}