{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:X4I7ZBHN5MTSXGO74NUMSUIL74","short_pith_number":"pith:X4I7ZBHN","canonical_record":{"source":{"id":"2310.20030","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-30T21:27:53Z","cross_cats_sorted":["math.DG","stat.ML"],"title_canon_sha256":"853b595212c121ae874f17ae9530d14f71a32dac8c138e50c64b3c18cf13e5df","abstract_canon_sha256":"088ef3a3ee19adaab5eaed2fcf693a8687b4787e39715b62496ccc2b9bbadebc"},"schema_version":"1.0"},"canonical_sha256":"bf11fc84edeb272b99dfe368c9510bff271e0f1f93f6790608dc8aff3ceb4692","source":{"kind":"arxiv","id":"2310.20030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.20030","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"arxiv_version","alias_value":"2310.20030v1","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.20030","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"pith_short_12","alias_value":"X4I7ZBHN5MTS","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"pith_short_16","alias_value":"X4I7ZBHN5MTSXGO7","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"pith_short_8","alias_value":"X4I7ZBHN","created_at":"2026-07-05T07:07:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:X4I7ZBHN5MTSXGO74NUMSUIL74","target":"record","payload":{"canonical_record":{"source":{"id":"2310.20030","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-30T21:27:53Z","cross_cats_sorted":["math.DG","stat.ML"],"title_canon_sha256":"853b595212c121ae874f17ae9530d14f71a32dac8c138e50c64b3c18cf13e5df","abstract_canon_sha256":"088ef3a3ee19adaab5eaed2fcf693a8687b4787e39715b62496ccc2b9bbadebc"},"schema_version":"1.0"},"canonical_sha256":"bf11fc84edeb272b99dfe368c9510bff271e0f1f93f6790608dc8aff3ceb4692","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:07:22.843383Z","signature_b64":"//uQJSlZntJkMo/Op5vn5Zz9qYEJ9bv2ACG1EiNURplUa9FIOffJ+PWkVWJUe4DVohhdZXLkMtGwh+kE2gKEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf11fc84edeb272b99dfe368c9510bff271e0f1f93f6790608dc8aff3ceb4692","last_reissued_at":"2026-07-05T07:07:22.842975Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:07:22.842975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2310.20030","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:07:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iSX+lIMODpBr1gJVZDwyXeruMbryXM26BvtAY66p6sm5FX38lv+Pq0LkfMS3gvAgy3stMXISgxmhxIz2FmsECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T16:22:48.501660Z"},"content_sha256":"9741e2c0bc2fb0e70627f313741c38eb10a62eb42f29dcb30fb4ea345a288d92","schema_version":"1.0","event_id":"sha256:9741e2c0bc2fb0e70627f313741c38eb10a62eb42f29dcb30fb4ea345a288d92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:X4I7ZBHN5MTSXGO74NUMSUIL74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scaling Riemannian Diffusion Models","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DG","stat.ML"],"primary_cat":"cs.LG","authors_text":"Aaron Lou, Minkai Xu, Stefano Ermon","submitted_at":"2023-10-30T21:27:53Z","abstract_excerpt":"Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.20030","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/2310.20030/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":"2026-07-05T07:07:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YUeDMy68q2dXBGyFjDFF6FF0y4kQPArn9dhVsDwNXRgMZuN0OlAftQjFfOtxHZP4y6OeFQCge+Y0C8wz+QbaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-22T16:22:48.502162Z"},"content_sha256":"53e2b46514284e35e0fcb59fb699036cbc30cc76636802a75d05922b8094e2f4","schema_version":"1.0","event_id":"sha256:53e2b46514284e35e0fcb59fb699036cbc30cc76636802a75d05922b8094e2f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X4I7ZBHN5MTSXGO74NUMSUIL74/bundle.json","state_url":"https://pith.science/pith/X4I7ZBHN5MTSXGO74NUMSUIL74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X4I7ZBHN5MTSXGO74NUMSUIL74/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":"2026-07-22T16:22:48Z","links":{"resolver":"https://pith.science/pith/X4I7ZBHN5MTSXGO74NUMSUIL74","bundle":"https://pith.science/pith/X4I7ZBHN5MTSXGO74NUMSUIL74/bundle.json","state":"https://pith.science/pith/X4I7ZBHN5MTSXGO74NUMSUIL74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X4I7ZBHN5MTSXGO74NUMSUIL74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:X4I7ZBHN5MTSXGO74NUMSUIL74","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":"088ef3a3ee19adaab5eaed2fcf693a8687b4787e39715b62496ccc2b9bbadebc","cross_cats_sorted":["math.DG","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-30T21:27:53Z","title_canon_sha256":"853b595212c121ae874f17ae9530d14f71a32dac8c138e50c64b3c18cf13e5df"},"schema_version":"1.0","source":{"id":"2310.20030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.20030","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"arxiv_version","alias_value":"2310.20030v1","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.20030","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"pith_short_12","alias_value":"X4I7ZBHN5MTS","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"pith_short_16","alias_value":"X4I7ZBHN5MTSXGO7","created_at":"2026-07-05T07:07:22Z"},{"alias_kind":"pith_short_8","alias_value":"X4I7ZBHN","created_at":"2026-07-05T07:07:22Z"}],"graph_snapshots":[{"event_id":"sha256:53e2b46514284e35e0fcb59fb699036cbc30cc76636802a75d05922b8094e2f4","target":"graph","created_at":"2026-07-05T07:07:22Z","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/2310.20030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Riemannian diffusion models draw inspiration from standard Euclidean space diffusion models to learn distributions on general manifolds. Unfortunately, the additional geometric complexity renders the diffusion transition term inexpressible in closed form, so prior methods resort to imprecise approximations of the score matching training objective that degrade performance and preclude applications in high dimensions. In this work, we reexamine these approximations and propose several practical improvements. Our key observation is that most relevant manifolds are symmetric spaces, which are much","authors_text":"Aaron Lou, Minkai Xu, Stefano Ermon","cross_cats":["math.DG","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-30T21:27:53Z","title":"Scaling Riemannian Diffusion Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.20030","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":"sha256:9741e2c0bc2fb0e70627f313741c38eb10a62eb42f29dcb30fb4ea345a288d92","target":"record","created_at":"2026-07-05T07:07:22Z","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":"088ef3a3ee19adaab5eaed2fcf693a8687b4787e39715b62496ccc2b9bbadebc","cross_cats_sorted":["math.DG","stat.ML"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2023-10-30T21:27:53Z","title_canon_sha256":"853b595212c121ae874f17ae9530d14f71a32dac8c138e50c64b3c18cf13e5df"},"schema_version":"1.0","source":{"id":"2310.20030","kind":"arxiv","version":1}},"canonical_sha256":"bf11fc84edeb272b99dfe368c9510bff271e0f1f93f6790608dc8aff3ceb4692","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf11fc84edeb272b99dfe368c9510bff271e0f1f93f6790608dc8aff3ceb4692","first_computed_at":"2026-07-05T07:07:22.842975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:07:22.842975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"//uQJSlZntJkMo/Op5vn5Zz9qYEJ9bv2ACG1EiNURplUa9FIOffJ+PWkVWJUe4DVohhdZXLkMtGwh+kE2gKEBw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:07:22.843383Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.20030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9741e2c0bc2fb0e70627f313741c38eb10a62eb42f29dcb30fb4ea345a288d92","sha256:53e2b46514284e35e0fcb59fb699036cbc30cc76636802a75d05922b8094e2f4"],"state_sha256":"6ff8dc34b4e9a4e9b1275551776e481f23119d9a093703808a7ba32e4455010a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TX8Dj1pAHkJ8XKtm+GLb3Dg7ZCdkV6z2lHecBzTL2K07omxJRLbDVFlhH5ptFQ/KRKYNLY+gZKAy4SNA7EQjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-22T16:22:48.504916Z","bundle_sha256":"27ff61649f4d1bbb46731c912f864bef0641283389beaf3249eae6c4b160206c"}}