{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:RK3T5GTBK6XNZC7RGIJM5SQV7A","short_pith_number":"pith:RK3T5GTB","canonical_record":{"source":{"id":"2601.18728","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-01-26T17:51:52Z","cross_cats_sorted":["math.DG","math.OC","math.ST","stat.TH"],"title_canon_sha256":"cbf95f2bb04ad08b3fbeee78d59a638a626e1d4d54399f29bc029728fab008ed","abstract_canon_sha256":"b238978f1725c4cc80caa68ff130c57ee25f886febcf6385551cb439ee696290"},"schema_version":"1.0"},"canonical_sha256":"8ab73e9a6157aedc8bf13212ceca15f82fc01e17e5924be7a860620b0cbee7b7","source":{"kind":"arxiv","id":"2601.18728","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.18728","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"2601.18728v2","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.18728","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"RK3T5GTBK6XN","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"pith_short_16","alias_value":"RK3T5GTBK6XNZC7R","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"pith_short_8","alias_value":"RK3T5GTB","created_at":"2026-05-29T01:04:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:RK3T5GTBK6XNZC7RGIJM5SQV7A","target":"record","payload":{"canonical_record":{"source":{"id":"2601.18728","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-01-26T17:51:52Z","cross_cats_sorted":["math.DG","math.OC","math.ST","stat.TH"],"title_canon_sha256":"cbf95f2bb04ad08b3fbeee78d59a638a626e1d4d54399f29bc029728fab008ed","abstract_canon_sha256":"b238978f1725c4cc80caa68ff130c57ee25f886febcf6385551cb439ee696290"},"schema_version":"1.0"},"canonical_sha256":"8ab73e9a6157aedc8bf13212ceca15f82fc01e17e5924be7a860620b0cbee7b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T01:04:36.531055Z","signature_b64":"fYXslD55sOWAPhGL7C+XjbitR401FwxNIrVJzTV46IAfLZinBbgGI+82FVCBM+fXe+QScTrbYPERLHCU+YC7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ab73e9a6157aedc8bf13212ceca15f82fc01e17e5924be7a860620b0cbee7b7","last_reissued_at":"2026-05-29T01:04:36.530428Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T01:04:36.530428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2601.18728","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T01:04:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Rw9lJhC3kv04bCw7iLzjUeW2FuZC5G/xmxrpXhLppADuv3a1prz+v8zo3cC1t1FXAqk5nVa05YDIcwlZiQhDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T23:23:31.669523Z"},"content_sha256":"149bd832d91cc589ab23a3ed77eb3582512b2c64df7c09277c0505583df4bfc1","schema_version":"1.0","event_id":"sha256:149bd832d91cc589ab23a3ed77eb3582512b2c64df7c09277c0505583df4bfc1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:RK3T5GTBK6XNZC7RGIJM5SQV7A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Data","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.DG","math.OC","math.ST","stat.TH"],"primary_cat":"cs.LG","authors_text":"Oscar Leong, Willem Diepeveen","submitted_at":"2026-01-26T17:51:52Z","abstract_excerpt":"Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or linearly corrupted measurements can be observed. Moreover, latent structures, such as manifold geometries, present in the data are important to extract for further downstream scientific analysis. In this work, we introduce Riemannian AmbientFlow, a framework for simultaneously learning a probabilistic generative model and the underlying, nonlinear data manifold di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.18728","kind":"arxiv","version":2},"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/2601.18728/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-29T01:04:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B7OqkC4RU6sJBa1bYr01GBM/YTyjPlL2+2sycDCy+E5lSN6wTlNWJZvRrq3XuZ/gDsriXj0Isx3HMDaHqOEWDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-29T23:23:31.670276Z"},"content_sha256":"4a9283460af73a9df957b1783a14138f48d6701037e8fa704144986e3b6a9637","schema_version":"1.0","event_id":"sha256:4a9283460af73a9df957b1783a14138f48d6701037e8fa704144986e3b6a9637"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RK3T5GTBK6XNZC7RGIJM5SQV7A/bundle.json","state_url":"https://pith.science/pith/RK3T5GTBK6XNZC7RGIJM5SQV7A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RK3T5GTBK6XNZC7RGIJM5SQV7A/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-29T23:23:31Z","links":{"resolver":"https://pith.science/pith/RK3T5GTBK6XNZC7RGIJM5SQV7A","bundle":"https://pith.science/pith/RK3T5GTBK6XNZC7RGIJM5SQV7A/bundle.json","state":"https://pith.science/pith/RK3T5GTBK6XNZC7RGIJM5SQV7A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RK3T5GTBK6XNZC7RGIJM5SQV7A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RK3T5GTBK6XNZC7RGIJM5SQV7A","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":"b238978f1725c4cc80caa68ff130c57ee25f886febcf6385551cb439ee696290","cross_cats_sorted":["math.DG","math.OC","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-01-26T17:51:52Z","title_canon_sha256":"cbf95f2bb04ad08b3fbeee78d59a638a626e1d4d54399f29bc029728fab008ed"},"schema_version":"1.0","source":{"id":"2601.18728","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.18728","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"arxiv_version","alias_value":"2601.18728v2","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.18728","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"pith_short_12","alias_value":"RK3T5GTBK6XN","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"pith_short_16","alias_value":"RK3T5GTBK6XNZC7R","created_at":"2026-05-29T01:04:36Z"},{"alias_kind":"pith_short_8","alias_value":"RK3T5GTB","created_at":"2026-05-29T01:04:36Z"}],"graph_snapshots":[{"event_id":"sha256:4a9283460af73a9df957b1783a14138f48d6701037e8fa704144986e3b6a9637","target":"graph","created_at":"2026-05-29T01:04:36Z","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/2601.18728/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Modern generative modeling methods have demonstrated strong performance in learning complex data distributions from clean samples. In many scientific and imaging applications, however, clean samples are unavailable, and only noisy or linearly corrupted measurements can be observed. Moreover, latent structures, such as manifold geometries, present in the data are important to extract for further downstream scientific analysis. In this work, we introduce Riemannian AmbientFlow, a framework for simultaneously learning a probabilistic generative model and the underlying, nonlinear data manifold di","authors_text":"Oscar Leong, Willem Diepeveen","cross_cats":["math.DG","math.OC","math.ST","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-01-26T17:51:52Z","title":"Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.18728","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":"sha256:149bd832d91cc589ab23a3ed77eb3582512b2c64df7c09277c0505583df4bfc1","target":"record","created_at":"2026-05-29T01:04:36Z","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":"b238978f1725c4cc80caa68ff130c57ee25f886febcf6385551cb439ee696290","cross_cats_sorted":["math.DG","math.OC","math.ST","stat.TH"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-01-26T17:51:52Z","title_canon_sha256":"cbf95f2bb04ad08b3fbeee78d59a638a626e1d4d54399f29bc029728fab008ed"},"schema_version":"1.0","source":{"id":"2601.18728","kind":"arxiv","version":2}},"canonical_sha256":"8ab73e9a6157aedc8bf13212ceca15f82fc01e17e5924be7a860620b0cbee7b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ab73e9a6157aedc8bf13212ceca15f82fc01e17e5924be7a860620b0cbee7b7","first_computed_at":"2026-05-29T01:04:36.530428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:04:36.530428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fYXslD55sOWAPhGL7C+XjbitR401FwxNIrVJzTV46IAfLZinBbgGI+82FVCBM+fXe+QScTrbYPERLHCU+YC7DQ==","signature_status":"signed_v1","signed_at":"2026-05-29T01:04:36.531055Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.18728","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:149bd832d91cc589ab23a3ed77eb3582512b2c64df7c09277c0505583df4bfc1","sha256:4a9283460af73a9df957b1783a14138f48d6701037e8fa704144986e3b6a9637"],"state_sha256":"c6be1deca000974087db2e9b4ecc66f0ad7347acaa31580c5401436f083e9c50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IFzXOjtLWGQ4qzQpYvDLf36Hx97OUAO+H+ECtFS2Tu7WRkqEFKfbz8EUhzRlX4w5A7vqcDc+DuVF830gH1jEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-29T23:23:31.675209Z","bundle_sha256":"ebcfc204fa67d1eddd4c9c6bade28cdf2f9a08e792830096287c1124ec501675"}}