{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:2DXGQ2KMBX5CKJP76PCMYQG6YM","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":"f00415ce34d16cac79634ad21c8ecc43427460e69b2deec40c7fdf2b9ad4ebe7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-05T23:29:06Z","title_canon_sha256":"ef13fab620dca6fec8a1a7103ed8a7b7fce91844390568388763a40cb79eeaf2"},"schema_version":"1.0","source":{"id":"2503.03963","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.03963","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"2503.03963v2","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.03963","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"2DXGQ2KMBX5C","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"pith_short_16","alias_value":"2DXGQ2KMBX5CKJP7","created_at":"2026-07-05T10:51:05Z"},{"alias_kind":"pith_short_8","alias_value":"2DXGQ2KM","created_at":"2026-07-05T10:51:05Z"}],"graph_snapshots":[{"event_id":"sha256:fd3e1082545b55b95beba75e61d46fb17d92c0744170a00803e183ee39e55dd5","target":"graph","created_at":"2026-07-05T10:51:05Z","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/2503.03963/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an It\\^o stochastic differential equation in th","authors_text":"Dimitris G. Giovanis, Ellis Crabtree, Ioannis G. Kevrekidis, Roger G. Ghanem","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-05T23:29:06Z","title":"Generative Learning of Densities on Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.03963","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:e53d42f852dc8e2ff19d6b342b67485bfb9c92efec1a5b2d0d6888e9e97851e7","target":"record","created_at":"2026-07-05T10:51:05Z","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":"f00415ce34d16cac79634ad21c8ecc43427460e69b2deec40c7fdf2b9ad4ebe7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2025-03-05T23:29:06Z","title_canon_sha256":"ef13fab620dca6fec8a1a7103ed8a7b7fce91844390568388763a40cb79eeaf2"},"schema_version":"1.0","source":{"id":"2503.03963","kind":"arxiv","version":2}},"canonical_sha256":"d0ee68694c0dfa2525fff3c4cc40dec316b9083546ef1d13765d61421c9c028e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0ee68694c0dfa2525fff3c4cc40dec316b9083546ef1d13765d61421c9c028e","first_computed_at":"2026-07-05T10:51:05.459344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:51:05.459344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EcpWj1rOCLljq8o7tCI8qppnVThDHtKoARtc+fD+osyMG+aUWxpyIJ6p0k5coYgqdkRW7FxfJZe2os7ICFkaDw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:51:05.459860Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.03963","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e53d42f852dc8e2ff19d6b342b67485bfb9c92efec1a5b2d0d6888e9e97851e7","sha256:fd3e1082545b55b95beba75e61d46fb17d92c0744170a00803e183ee39e55dd5"],"state_sha256":"5f496c0907bb4407230fe8522b4c666917f52d9e438d9f28be551801b5d11c55"}