{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:3LROK2Z36AVBBSTCJX5DRVN5O4","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":"f416adbca93020dc919f0726d27dc5c6a9d5b90ac38d7319e6b311da3ae3a713","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2020-10-05T16:23:04Z","title_canon_sha256":"15a5929b3bd502c6d2dcf6c04908c3591378fffc2855192cb740108cc6351a7b"},"schema_version":"1.0","source":{"id":"2010.02131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.02131","created_at":"2026-07-05T01:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"2010.02131v1","created_at":"2026-07-05T01:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.02131","created_at":"2026-07-05T01:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"3LROK2Z36AVB","created_at":"2026-07-05T01:40:17Z"},{"alias_kind":"pith_short_16","alias_value":"3LROK2Z36AVBBSTC","created_at":"2026-07-05T01:40:17Z"},{"alias_kind":"pith_short_8","alias_value":"3LROK2Z3","created_at":"2026-07-05T01:40:17Z"}],"graph_snapshots":[{"event_id":"sha256:01ed8c26545b434fccedc9dbe056760980822f4f633d023109689bd77bce1f35","target":"graph","created_at":"2026-07-05T01:40:17Z","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/2010.02131/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 ","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)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2020-10-05T16:23:04Z","title":"Differentiable maps between Wasserstein spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.02131","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:a68794ebaa94552a7ddbdfaac9e4a357b0b79d076965dbb2a6fa106bc564d93f","target":"record","created_at":"2026-07-05T01:40:17Z","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":"f416adbca93020dc919f0726d27dc5c6a9d5b90ac38d7319e6b311da3ae3a713","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2020-10-05T16:23:04Z","title_canon_sha256":"15a5929b3bd502c6d2dcf6c04908c3591378fffc2855192cb740108cc6351a7b"},"schema_version":"1.0","source":{"id":"2010.02131","kind":"arxiv","version":1}},"canonical_sha256":"dae2e56b3bf02a10ca624dfa38d5bd7737cfe644dff23c9840423d60288251e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dae2e56b3bf02a10ca624dfa38d5bd7737cfe644dff23c9840423d60288251e5","first_computed_at":"2026-07-05T01:40:17.717363Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:40:17.717363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N05us9JTjvmroowRitsjk33vC5aLvyU83azol6EcWRgygdYCrwzPcXYA092/MB/AV0bLDgrVACCQv0WPUdn8AA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:40:17.717755Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.02131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a68794ebaa94552a7ddbdfaac9e4a357b0b79d076965dbb2a6fa106bc564d93f","sha256:01ed8c26545b434fccedc9dbe056760980822f4f633d023109689bd77bce1f35"],"state_sha256":"b078042432f691282d0010ac71ae6c5321e38cc4ce28ec92a434e025bbee4b1f"}