{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:SHOBFUC67AC6JMLLUQXAWWOHLW","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":"1d82f9c353cd4bac4ae7ee74df3d54b026d88698872e555ad433728ec1696c37","cross_cats_sorted":["math.AP","math.DG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-20T09:07:25Z","title_canon_sha256":"2acd53a3e43f3c1c17d66934c2acdcf52e9205d8e4ea4b71e5fb4648272e4c0b"},"schema_version":"1.0","source":{"id":"1009.3737","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3737","created_at":"2026-05-18T04:40:43Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3737v1","created_at":"2026-05-18T04:40:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3737","created_at":"2026-05-18T04:40:43Z"},{"alias_kind":"pith_short_12","alias_value":"SHOBFUC67AC6","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"SHOBFUC67AC6JMLL","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"SHOBFUC6","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:1aa1e7a065ffc6786c44ad1e8fe9badbe08395932734e4a02f1f2db89f9d0b1c","target":"graph","created_at":"2026-05-18T04:40:43Z","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":"We present a short overview on the strongest variational formulation for gradient flows of geodesically $\\lambda$-convex functionals in metric spaces, with applications to diffusion equations in Wasserstein spaces of probability measures. These notes are based on a series of lectures given by the second author for the Summer School \"Optimal transportation: Theory and applications\" in Grenoble during the week of June 22-26, 2009.","authors_text":"Giuseppe Savar\\'e, Sara Daneri (SISSA/ISAS)","cross_cats":["math.AP","math.DG","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-20T09:07:25Z","title":"Lecture Notes on Gradient Flows and Optimal Transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3737","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:b5cab1e4715b5f436c702250baad56247bfbd8812f1dad66f58e2c9057db5414","target":"record","created_at":"2026-05-18T04:40:43Z","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":"1d82f9c353cd4bac4ae7ee74df3d54b026d88698872e555ad433728ec1696c37","cross_cats_sorted":["math.AP","math.DG","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2010-09-20T09:07:25Z","title_canon_sha256":"2acd53a3e43f3c1c17d66934c2acdcf52e9205d8e4ea4b71e5fb4648272e4c0b"},"schema_version":"1.0","source":{"id":"1009.3737","kind":"arxiv","version":1}},"canonical_sha256":"91dc12d05ef805e4b16ba42e0b59c75db14739fb6bbb390bace83543bb2b5881","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91dc12d05ef805e4b16ba42e0b59c75db14739fb6bbb390bace83543bb2b5881","first_computed_at":"2026-05-18T04:40:43.967454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:43.967454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZB9AvrQ4PlMriTTK0DMNSHirkZCYHJiOU89kRkdApwfZCpBA1q65d9zZpweMN03GxoJXh9Ad53U1Rh/Wf17HDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:43.968156Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3737","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5cab1e4715b5f436c702250baad56247bfbd8812f1dad66f58e2c9057db5414","sha256:1aa1e7a065ffc6786c44ad1e8fe9badbe08395932734e4a02f1f2db89f9d0b1c"],"state_sha256":"204e0eb3e156e698712c9d4a27ef35ef8c6015ee843b4815cde1c820ea97e07c"}