{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:3LROK2Z36AVBBSTCJX5DRVN5O4","short_pith_number":"pith:3LROK2Z3","schema_version":"1.0","canonical_sha256":"dae2e56b3bf02a10ca624dfa38d5bd7737cfe644dff23c9840423d60288251e5","source":{"kind":"arxiv","id":"2010.02131","version":1},"attestation_state":"computed","paper":{"title":"Differentiable maps between Wasserstein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Berlin (2) Mathematisches Institut, Bernadette Lessel (1), Thomas Schick (2) ((1) Max Planck Institute for the History of Science, Universit\\\"at G\\\"ottingen)","submitted_at":"2020-10-05T16:23:04Z","abstract_excerpt":"A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a global definition of differentiability, i.e. without a prior notion of pointwise differentiability. With our definition, however, we recover the expected properties of a differential. Special focus is being put on differentiability properties of pushforward maps induced by smooth maps between the underlying manifolds, and on convex mixing of differentiable "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2010.02131","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2020-10-05T16:23:04Z","cross_cats_sorted":[],"title_canon_sha256":"15a5929b3bd502c6d2dcf6c04908c3591378fffc2855192cb740108cc6351a7b","abstract_canon_sha256":"f416adbca93020dc919f0726d27dc5c6a9d5b90ac38d7319e6b311da3ae3a713"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:40:17.717755Z","signature_b64":"N05us9JTjvmroowRitsjk33vC5aLvyU83azol6EcWRgygdYCrwzPcXYA092/MB/AV0bLDgrVACCQv0WPUdn8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dae2e56b3bf02a10ca624dfa38d5bd7737cfe644dff23c9840423d60288251e5","last_reissued_at":"2026-07-05T01:40:17.717363Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:40:17.717363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Differentiable maps between Wasserstein spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Berlin (2) Mathematisches Institut, Bernadette Lessel (1), Thomas Schick (2) ((1) Max Planck Institute for the History of Science, Universit\\\"at G\\\"ottingen)","submitted_at":"2020-10-05T16:23:04Z","abstract_excerpt":"A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a global definition of differentiability, i.e. without a prior notion of pointwise differentiability. With our definition, however, we recover the expected properties of a differential. Special focus is being put on differentiability properties of pushforward maps induced by smooth maps between the underlying manifolds, and on convex mixing of differentiable "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.02131","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.02131/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2010.02131","created_at":"2026-07-05T01:40:17.717424+00:00"},{"alias_kind":"arxiv_version","alias_value":"2010.02131v1","created_at":"2026-07-05T01:40:17.717424+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.02131","created_at":"2026-07-05T01:40:17.717424+00:00"},{"alias_kind":"pith_short_12","alias_value":"3LROK2Z36AVB","created_at":"2026-07-05T01:40:17.717424+00:00"},{"alias_kind":"pith_short_16","alias_value":"3LROK2Z36AVBBSTC","created_at":"2026-07-05T01:40:17.717424+00:00"},{"alias_kind":"pith_short_8","alias_value":"3LROK2Z3","created_at":"2026-07-05T01:40:17.717424+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3LROK2Z36AVBBSTCJX5DRVN5O4","json":"https://pith.science/pith/3LROK2Z36AVBBSTCJX5DRVN5O4.json","graph_json":"https://pith.science/api/pith-number/3LROK2Z36AVBBSTCJX5DRVN5O4/graph.json","events_json":"https://pith.science/api/pith-number/3LROK2Z36AVBBSTCJX5DRVN5O4/events.json","paper":"https://pith.science/paper/3LROK2Z3"},"agent_actions":{"view_html":"https://pith.science/pith/3LROK2Z36AVBBSTCJX5DRVN5O4","download_json":"https://pith.science/pith/3LROK2Z36AVBBSTCJX5DRVN5O4.json","view_paper":"https://pith.science/paper/3LROK2Z3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2010.02131&json=true","fetch_graph":"https://pith.science/api/pith-number/3LROK2Z36AVBBSTCJX5DRVN5O4/graph.json","fetch_events":"https://pith.science/api/pith-number/3LROK2Z36AVBBSTCJX5DRVN5O4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3LROK2Z36AVBBSTCJX5DRVN5O4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3LROK2Z36AVBBSTCJX5DRVN5O4/action/storage_attestation","attest_author":"https://pith.science/pith/3LROK2Z36AVBBSTCJX5DRVN5O4/action/author_attestation","sign_citation":"https://pith.science/pith/3LROK2Z36AVBBSTCJX5DRVN5O4/action/citation_signature","submit_replication":"https://pith.science/pith/3LROK2Z36AVBBSTCJX5DRVN5O4/action/replication_record"}},"created_at":"2026-07-05T01:40:17.717424+00:00","updated_at":"2026-07-05T01:40:17.717424+00:00"}