{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:L32P5GM5YKTIN3FGHZGUZC3KMT","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":"8001b10416084e85976f17f6e4186d8e04b93e39783d61aba7bd0aeb1c0ff2bc","cross_cats_sorted":["cs.LG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-11-14T21:21:35Z","title_canon_sha256":"370eb7b9fb373316192f72f60ee49a0e662aa242fe665234ababea5f0d16d644"},"schema_version":"1.0","source":{"id":"2311.08549","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.08549","created_at":"2026-07-05T10:40:57Z"},{"alias_kind":"arxiv_version","alias_value":"2311.08549v3","created_at":"2026-07-05T10:40:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.08549","created_at":"2026-07-05T10:40:57Z"},{"alias_kind":"pith_short_12","alias_value":"L32P5GM5YKTI","created_at":"2026-07-05T10:40:57Z"},{"alias_kind":"pith_short_16","alias_value":"L32P5GM5YKTIN3FG","created_at":"2026-07-05T10:40:57Z"},{"alias_kind":"pith_short_8","alias_value":"L32P5GM5","created_at":"2026-07-05T10:40:57Z"}],"graph_snapshots":[{"event_id":"sha256:c71ae13a635af586504316af972e536b72c5adaf30fe2bbe4ca4533885944b5b","target":"graph","created_at":"2026-07-05T10:40:57Z","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/2311.08549/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper aims at building the theoretical foundations for manifold learning algorithms in the space of absolutely continuous probability measures $\\mathcal{P}_{\\mathrm{a.c.}}(\\Omega)$ with $\\Omega$ a compact and convex subset of $\\mathbb{R}^d$, metrized with the Wasserstein-2 distance $\\mathbb{W}$. We begin by introducing a construction of submanifolds $\\Lambda$ in $\\mathcal{P}_{\\mathrm{a.c.}}(\\Omega)$ equipped with metric $\\mathbb{W}_\\Lambda$, the geodesic restriction of $\\mathbb{W}$ to $\\Lambda$. In contrast to other constructions, these submanifolds are not necessarily flat, but still all","authors_text":"Bernhard Schmitzer, Caroline Moosm\\\"uller, Keaton Hamm, Matthew Thorpe","cross_cats":["cs.LG","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-11-14T21:21:35Z","title":"Manifold learning in Wasserstein space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.08549","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":"sha256:30d61dc9bbed38afac0dc8b75518ffbf20097e02fdd8fa983937e0c97d6559c2","target":"record","created_at":"2026-07-05T10:40:57Z","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":"8001b10416084e85976f17f6e4186d8e04b93e39783d61aba7bd0aeb1c0ff2bc","cross_cats_sorted":["cs.LG","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ML","submitted_at":"2023-11-14T21:21:35Z","title_canon_sha256":"370eb7b9fb373316192f72f60ee49a0e662aa242fe665234ababea5f0d16d644"},"schema_version":"1.0","source":{"id":"2311.08549","kind":"arxiv","version":3}},"canonical_sha256":"5ef4fe999dc2a686eca63e4d4c8b6a64e4b61bc2acff58162102bca36a7c746f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ef4fe999dc2a686eca63e4d4c8b6a64e4b61bc2acff58162102bca36a7c746f","first_computed_at":"2026-07-05T10:40:57.580845Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:40:57.580845Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K3u3fcqcRzafQZywRd6H44JneFM+4uLRyyq6MgzB8AZ4ugHI5cIHNa0tq/2YLM+ML7OVW1Z8y+AZApijzLd1Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:40:57.581357Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.08549","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30d61dc9bbed38afac0dc8b75518ffbf20097e02fdd8fa983937e0c97d6559c2","sha256:c71ae13a635af586504316af972e536b72c5adaf30fe2bbe4ca4533885944b5b"],"state_sha256":"651b85b9b1c045bb0f3c61151b45b4c6a3047a18db45aa6afbeb81008fd5b047"}