{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:I3TXIT2ZWMTLC2A3ICGEVTKZLR","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":"44c7f155c20aa6e282df5c36c757e31859b31204e70d789339e57f32d0ca6eb7","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-11-05T17:07:46Z","title_canon_sha256":"d7b7dc481df4e8a0a67b9d2ccc4982c3288da1edd44bef91b4195668e9a80ad3"},"schema_version":"1.0","source":{"id":"2411.03265","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.03265","created_at":"2026-07-05T09:41:03Z"},{"alias_kind":"arxiv_version","alias_value":"2411.03265v2","created_at":"2026-07-05T09:41:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.03265","created_at":"2026-07-05T09:41:03Z"},{"alias_kind":"pith_short_12","alias_value":"I3TXIT2ZWMTL","created_at":"2026-07-05T09:41:03Z"},{"alias_kind":"pith_short_16","alias_value":"I3TXIT2ZWMTLC2A3","created_at":"2026-07-05T09:41:03Z"},{"alias_kind":"pith_short_8","alias_value":"I3TXIT2Z","created_at":"2026-07-05T09:41:03Z"}],"graph_snapshots":[{"event_id":"sha256:b571ea36a9b53029493fe852a6cb728bf9b5e30fd442f436dada983d700f7435","target":"graph","created_at":"2026-07-05T09:41:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.03265/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The study of diffeomorphism groups and their applications to problems in analysis and geometry has a long history. In geometric hydrodynamics, pioneered by V.~Arnold in the 1960s, one considers an ideal fluid flow as the geodesic motion on the infinite-dimensional group of volume-preserving diffeomorphisms of the fluid domain with respect to the metric defined by the kinetic energy. Similar considerations on the space of densities lead to a geometric description of optimal mass transport and the Kantorovich-Wasserstein metric. Likewise, information geometry associated with the Fisher-Rao metri","authors_text":"Boris Khesin, Gerard Misio{\\l}ek, Klas Modin","cross_cats":["cs.IT","math-ph","math.IT","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-11-05T17:07:46Z","title":"Information geometry of diffeomorphism groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03265","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":"sha256:450853cbed99b23aa6217b9d5d394395cbd04e9a21097669d948e9be267c72a2","target":"record","created_at":"2026-07-05T09:41:03Z","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":"44c7f155c20aa6e282df5c36c757e31859b31204e70d789339e57f32d0ca6eb7","cross_cats_sorted":["cs.IT","math-ph","math.IT","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-11-05T17:07:46Z","title_canon_sha256":"d7b7dc481df4e8a0a67b9d2ccc4982c3288da1edd44bef91b4195668e9a80ad3"},"schema_version":"1.0","source":{"id":"2411.03265","kind":"arxiv","version":2}},"canonical_sha256":"46e7744f59b326b1681b408c4acd595c7d906a3b22006d059ed4637906a7acfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46e7744f59b326b1681b408c4acd595c7d906a3b22006d059ed4637906a7acfa","first_computed_at":"2026-07-05T09:41:03.309053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:41:03.309053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2QrNGoRpDgR9qH7vQ5xV09GISLsbFvJMtvFcX1bi8SQQcqozLSHuB07jakS9STXlrrsBjOwcGHwD9XjSCDAWDA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:41:03.309492Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.03265","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:450853cbed99b23aa6217b9d5d394395cbd04e9a21097669d948e9be267c72a2","sha256:b571ea36a9b53029493fe852a6cb728bf9b5e30fd442f436dada983d700f7435"],"state_sha256":"fbf5f68e5eb5426361a485f702cc017a8b5972e21a0f8523ec2b121a26751ae5"}