{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DQJL5XEUXKMZUAXZ6K6PHFXOLE","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":"bc86a1030d29efe952952ba7863e7f36095ba0a17a08ca8fec94265941f2178f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-11T13:52:07Z","title_canon_sha256":"44c98ae47d4072cdc37270be1ab7917c7936295bf5aa1af187649c0f9998a0aa"},"schema_version":"1.0","source":{"id":"1610.03339","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.03339","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"arxiv_version","alias_value":"1610.03339v3","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.03339","created_at":"2026-05-17T23:46:55Z"},{"alias_kind":"pith_short_12","alias_value":"DQJL5XEUXKMZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DQJL5XEUXKMZUAXZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DQJL5XEU","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:c6110c5c7992c0c48313bc8275bf7fb0fe25c232d3744f58134f5c30231ebf76","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":"The goal of the paper is to give an optimal transport characterization of sectional curvature lower (and upper) bounds for smooth $n$-dimensional Riemannian manifolds. More generally we characterize, via optimal transport, lower bounds on the so called $p$-Ricci curvature which corresponds to taking the trace of the Riemann curvature tensor on $p$-dimensional planes, $1\\leq p\\leq n$. Such characterization roughly consists on a convexity condition of the $p$-Renyi entropy along $L^{2}$-Wasserstein geodesics, where the role of reference measure is played by the $p$-dimensional Hausdorff measure.","authors_text":"Andrea Mondino, Christian Ketterer","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-11T13:52:07Z","title":"Sectional and intermediate Ricci curvature lower bounds via Optimal Transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.03339","kind":"arxiv","version":3},"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":"sha256:4e00d6d11e8278b11be153ce594b30b635b6393d13e3940d4412c2709d4d3474","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":"bc86a1030d29efe952952ba7863e7f36095ba0a17a08ca8fec94265941f2178f","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-11T13:52:07Z","title_canon_sha256":"44c98ae47d4072cdc37270be1ab7917c7936295bf5aa1af187649c0f9998a0aa"},"schema_version":"1.0","source":{"id":"1610.03339","kind":"arxiv","version":3}},"canonical_sha256":"1c12bedc94ba999a02f9f2bcf396ee592d2878360a459c180d22247b20b279e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c12bedc94ba999a02f9f2bcf396ee592d2878360a459c180d22247b20b279e6","first_computed_at":"2026-05-17T23:46:55.828738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:55.828738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PyJH8Aw/xaOi6F5qb7ZB7+Wkip4X5sAL1FIGuZBrYOiqyJfKCAf9oVOI4O8N+UcqhvtUlOjqkNnmj0+t5M+aBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:55.829159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.03339","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e00d6d11e8278b11be153ce594b30b635b6393d13e3940d4412c2709d4d3474","sha256:c6110c5c7992c0c48313bc8275bf7fb0fe25c232d3744f58134f5c30231ebf76"],"state_sha256":"5282636c0698b5c480af7093b4550613cddf5d5ba05163f2c5347a3830fcb15b"}