{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:SIPI2QNEEG7D6ABAUH7CHITDNI","short_pith_number":"pith:SIPI2QNE","canonical_record":{"source":{"id":"2102.00264","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-01-30T16:35:25Z","cross_cats_sorted":["cs.CV","math.GT"],"title_canon_sha256":"03408c385a8f8def64b4d0176d15e4c94cb042fc1828a681864dec6d8f52d94e","abstract_canon_sha256":"2be38920cd9c60a1d6ada9f5ea30fdd95ccd6e242f5571581f5a16d304c2b3af"},"schema_version":"1.0"},"canonical_sha256":"921e8d41a421be3f0020a1fe23a2636a0191c3e61ab117b3b6a50f1a481e151d","source":{"kind":"arxiv","id":"2102.00264","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.00264","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"2102.00264v2","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.00264","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"SIPI2QNEEG7D","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"pith_short_16","alias_value":"SIPI2QNEEG7D6ABA","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"pith_short_8","alias_value":"SIPI2QNE","created_at":"2026-07-05T04:06:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:SIPI2QNEEG7D6ABAUH7CHITDNI","target":"record","payload":{"canonical_record":{"source":{"id":"2102.00264","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-01-30T16:35:25Z","cross_cats_sorted":["cs.CV","math.GT"],"title_canon_sha256":"03408c385a8f8def64b4d0176d15e4c94cb042fc1828a681864dec6d8f52d94e","abstract_canon_sha256":"2be38920cd9c60a1d6ada9f5ea30fdd95ccd6e242f5571581f5a16d304c2b3af"},"schema_version":"1.0"},"canonical_sha256":"921e8d41a421be3f0020a1fe23a2636a0191c3e61ab117b3b6a50f1a481e151d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:06:41.236929Z","signature_b64":"u5gDcT2lzUT3ur+QBukSeSvoLmLWdmtrqdWFtMmZ3FqvlGj0EVkcZ2tcTrvP0VTb74zpa/3skgcQ4/dPouohCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"921e8d41a421be3f0020a1fe23a2636a0191c3e61ab117b3b6a50f1a481e151d","last_reissued_at":"2026-07-05T04:06:41.236522Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:06:41.236522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2102.00264","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":"2026-07-05T04:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2q5HOgxd0gVvDuklo260y5pp68qLVlU/EqnU5oo7g02ULvNwJemTAxsLVdPsTpTqS2uUkHjCBSh9tDIa1TiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:00:12.162991Z"},"content_sha256":"62333b3095eca8a29f22aed85b88afffc91a9ada52a8811b513e8e7cd7ea6c4f","schema_version":"1.0","event_id":"sha256:62333b3095eca8a29f22aed85b88afffc91a9ada52a8811b513e8e7cd7ea6c4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:SIPI2QNEEG7D6ABAUH7CHITDNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Atlas Generative Models and Geodesic Interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CV","math.GT"],"primary_cat":"cs.LG","authors_text":"Jakob Stolberg-Larsen, Stefan Sommer","submitted_at":"2021-01-30T16:35:25Z","abstract_excerpt":"Generative neural networks have a well recognized ability to estimate underlying manifold structure of high dimensional data. However, if a single latent space is used, it is not possible to faithfully represent a manifold with topology different from Euclidean space. In this work we define the general class of Atlas Generative Models (AGMs), models with hybrid discrete-continuous latent space that estimate an atlas on the underlying data manifold together with a partition of unity on the data space. We identify existing examples of models from various popular generative paradigms that fit int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.00264","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/2102.00264/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":"2026-07-05T04:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JiWpux3WEDZDBDsDqgJ70CrqljzgPDM0rbdxmjuif+6FpSROHTElUUOfvvGtfzH5RaKZuWDqkFbN+XNDeUiiAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T13:00:12.163613Z"},"content_sha256":"4d78353e728dbdced1789966165d9d923802f99b494ebaf8092333220ee2c28c","schema_version":"1.0","event_id":"sha256:4d78353e728dbdced1789966165d9d923802f99b494ebaf8092333220ee2c28c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SIPI2QNEEG7D6ABAUH7CHITDNI/bundle.json","state_url":"https://pith.science/pith/SIPI2QNEEG7D6ABAUH7CHITDNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SIPI2QNEEG7D6ABAUH7CHITDNI/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":"2026-08-06T13:00:12Z","links":{"resolver":"https://pith.science/pith/SIPI2QNEEG7D6ABAUH7CHITDNI","bundle":"https://pith.science/pith/SIPI2QNEEG7D6ABAUH7CHITDNI/bundle.json","state":"https://pith.science/pith/SIPI2QNEEG7D6ABAUH7CHITDNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SIPI2QNEEG7D6ABAUH7CHITDNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:SIPI2QNEEG7D6ABAUH7CHITDNI","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":"2be38920cd9c60a1d6ada9f5ea30fdd95ccd6e242f5571581f5a16d304c2b3af","cross_cats_sorted":["cs.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-01-30T16:35:25Z","title_canon_sha256":"03408c385a8f8def64b4d0176d15e4c94cb042fc1828a681864dec6d8f52d94e"},"schema_version":"1.0","source":{"id":"2102.00264","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2102.00264","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"2102.00264v2","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.00264","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"SIPI2QNEEG7D","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"pith_short_16","alias_value":"SIPI2QNEEG7D6ABA","created_at":"2026-07-05T04:06:41Z"},{"alias_kind":"pith_short_8","alias_value":"SIPI2QNE","created_at":"2026-07-05T04:06:41Z"}],"graph_snapshots":[{"event_id":"sha256:4d78353e728dbdced1789966165d9d923802f99b494ebaf8092333220ee2c28c","target":"graph","created_at":"2026-07-05T04:06:41Z","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/2102.00264/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Generative neural networks have a well recognized ability to estimate underlying manifold structure of high dimensional data. However, if a single latent space is used, it is not possible to faithfully represent a manifold with topology different from Euclidean space. In this work we define the general class of Atlas Generative Models (AGMs), models with hybrid discrete-continuous latent space that estimate an atlas on the underlying data manifold together with a partition of unity on the data space. We identify existing examples of models from various popular generative paradigms that fit int","authors_text":"Jakob Stolberg-Larsen, Stefan Sommer","cross_cats":["cs.CV","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-01-30T16:35:25Z","title":"Atlas Generative Models and Geodesic Interpolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.00264","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":"sha256:62333b3095eca8a29f22aed85b88afffc91a9ada52a8811b513e8e7cd7ea6c4f","target":"record","created_at":"2026-07-05T04:06:41Z","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":"2be38920cd9c60a1d6ada9f5ea30fdd95ccd6e242f5571581f5a16d304c2b3af","cross_cats_sorted":["cs.CV","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2021-01-30T16:35:25Z","title_canon_sha256":"03408c385a8f8def64b4d0176d15e4c94cb042fc1828a681864dec6d8f52d94e"},"schema_version":"1.0","source":{"id":"2102.00264","kind":"arxiv","version":2}},"canonical_sha256":"921e8d41a421be3f0020a1fe23a2636a0191c3e61ab117b3b6a50f1a481e151d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"921e8d41a421be3f0020a1fe23a2636a0191c3e61ab117b3b6a50f1a481e151d","first_computed_at":"2026-07-05T04:06:41.236522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:06:41.236522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u5gDcT2lzUT3ur+QBukSeSvoLmLWdmtrqdWFtMmZ3FqvlGj0EVkcZ2tcTrvP0VTb74zpa/3skgcQ4/dPouohCg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:06:41.236929Z","signed_message":"canonical_sha256_bytes"},"source_id":"2102.00264","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62333b3095eca8a29f22aed85b88afffc91a9ada52a8811b513e8e7cd7ea6c4f","sha256:4d78353e728dbdced1789966165d9d923802f99b494ebaf8092333220ee2c28c"],"state_sha256":"78be4f4221cf856685649e24cec326b1658f2601e04c183c454f2c51141c2db6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rXxoBNMZxqGcNIaqG9s2OOjATli7ynTHMFS3jsUfExA0j/GY+YAj7zcerCWr83llHf8KMOzP2hUAaiP0CY5ODA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T13:00:12.170527Z","bundle_sha256":"4c5d68c0dcb8199576ee5310836222c578261210d1f7d69f0d6d4b2529162d6d"}}