{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:HKP6A53K6FDVDGYEWDN6ICMOHM","short_pith_number":"pith:HKP6A53K","canonical_record":{"source":{"id":"2112.15595","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-31T18:57:37Z","cross_cats_sorted":["cs.LG","math.PR"],"title_canon_sha256":"9b922826c2a5b3b7d4a6820766faac58806e5fdb098200b65b6e5971ea489afc","abstract_canon_sha256":"1b7ee8aba4ec7246610d1def379bbde6eb70e0333e5435378b5e411d986b1dc0"},"schema_version":"1.0"},"canonical_sha256":"3a9fe0776af147519b04b0dbe4098e3b123f3a7318d60d3681c9b5eb78ff3837","source":{"kind":"arxiv","id":"2112.15595","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.15595","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"2112.15595v1","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.15595","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"HKP6A53K6FDV","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"pith_short_16","alias_value":"HKP6A53K6FDVDGYE","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"pith_short_8","alias_value":"HKP6A53K","created_at":"2026-07-05T03:44:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:HKP6A53K6FDVDGYEWDN6ICMOHM","target":"record","payload":{"canonical_record":{"source":{"id":"2112.15595","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-31T18:57:37Z","cross_cats_sorted":["cs.LG","math.PR"],"title_canon_sha256":"9b922826c2a5b3b7d4a6820766faac58806e5fdb098200b65b6e5971ea489afc","abstract_canon_sha256":"1b7ee8aba4ec7246610d1def379bbde6eb70e0333e5435378b5e411d986b1dc0"},"schema_version":"1.0"},"canonical_sha256":"3a9fe0776af147519b04b0dbe4098e3b123f3a7318d60d3681c9b5eb78ff3837","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:44:47.887744Z","signature_b64":"GK2+Ug/t8ow9XK844Aat2HD7kNQPuG9yd2OIA7HQDX6di78fMDPjZAfc6YkdeWry6P1vfSjyru/2vONrW8jjAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a9fe0776af147519b04b0dbe4098e3b123f3a7318d60d3681c9b5eb78ff3837","last_reissued_at":"2026-07-05T03:44:47.887391Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:44:47.887391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2112.15595","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":"2026-07-05T03:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/bPrKu3prKEL240xl8/hiqs2bW07NeHkvBpP+8OJBWCjTj7HKOE5kdDghk4L+rrMmVxxRJRjpQ1+XWMpK76GBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:19:58.650894Z"},"content_sha256":"152588a871538e9bc50afa52a144bbc3ec34dc3010a725a5594da18384df632a","schema_version":"1.0","event_id":"sha256:152588a871538e9bc50afa52a144bbc3ec34dc3010a725a5594da18384df632a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:HKP6A53K6FDVDGYEWDN6ICMOHM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Triangular Flows for Generative Modeling: Statistical Consistency, Smoothness Classes, and Fast Rates","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LG","math.PR"],"primary_cat":"stat.ML","authors_text":"Meyer Scetbon, Nicholas J. Irons, Soumik Pal, Zaid Harchaoui","submitted_at":"2021-12-31T18:57:37Z","abstract_excerpt":"Triangular flows, also known as Kn\\\"{o}the-Rosenblatt measure couplings, comprise an important building block of normalizing flow models for generative modeling and density estimation, including popular autoregressive flow models such as real-valued non-volume preserving transformation models (Real NVP). We present statistical guarantees and sample complexity bounds for triangular flow statistical models. In particular, we establish the statistical consistency and the finite sample convergence rates of the Kullback-Leibler estimator of the Kn\\\"{o}the-Rosenblatt measure coupling using tools fro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.15595","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/2112.15595/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":"2026-07-05T03:44:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z+2XkO90x174K8n++b/guyxftMkFE76RQgWfjQWxYkOwXC85opobWY3FMBOIqO/n4lxfN6h4B+4IP5C8bypIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T15:19:58.651482Z"},"content_sha256":"18bb19b158b903a31052f8339aeee36a564869364ab2c72e4595c0594ab01299","schema_version":"1.0","event_id":"sha256:18bb19b158b903a31052f8339aeee36a564869364ab2c72e4595c0594ab01299"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKP6A53K6FDVDGYEWDN6ICMOHM/bundle.json","state_url":"https://pith.science/pith/HKP6A53K6FDVDGYEWDN6ICMOHM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKP6A53K6FDVDGYEWDN6ICMOHM/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":"2026-08-18T15:19:58Z","links":{"resolver":"https://pith.science/pith/HKP6A53K6FDVDGYEWDN6ICMOHM","bundle":"https://pith.science/pith/HKP6A53K6FDVDGYEWDN6ICMOHM/bundle.json","state":"https://pith.science/pith/HKP6A53K6FDVDGYEWDN6ICMOHM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKP6A53K6FDVDGYEWDN6ICMOHM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:HKP6A53K6FDVDGYEWDN6ICMOHM","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":"1b7ee8aba4ec7246610d1def379bbde6eb70e0333e5435378b5e411d986b1dc0","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-31T18:57:37Z","title_canon_sha256":"9b922826c2a5b3b7d4a6820766faac58806e5fdb098200b65b6e5971ea489afc"},"schema_version":"1.0","source":{"id":"2112.15595","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2112.15595","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"arxiv_version","alias_value":"2112.15595v1","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2112.15595","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"pith_short_12","alias_value":"HKP6A53K6FDV","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"pith_short_16","alias_value":"HKP6A53K6FDVDGYE","created_at":"2026-07-05T03:44:47Z"},{"alias_kind":"pith_short_8","alias_value":"HKP6A53K","created_at":"2026-07-05T03:44:47Z"}],"graph_snapshots":[{"event_id":"sha256:18bb19b158b903a31052f8339aeee36a564869364ab2c72e4595c0594ab01299","target":"graph","created_at":"2026-07-05T03:44:47Z","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/2112.15595/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Triangular flows, also known as Kn\\\"{o}the-Rosenblatt measure couplings, comprise an important building block of normalizing flow models for generative modeling and density estimation, including popular autoregressive flow models such as real-valued non-volume preserving transformation models (Real NVP). We present statistical guarantees and sample complexity bounds for triangular flow statistical models. In particular, we establish the statistical consistency and the finite sample convergence rates of the Kullback-Leibler estimator of the Kn\\\"{o}the-Rosenblatt measure coupling using tools fro","authors_text":"Meyer Scetbon, Nicholas J. Irons, Soumik Pal, Zaid Harchaoui","cross_cats":["cs.LG","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-31T18:57:37Z","title":"Triangular Flows for Generative Modeling: Statistical Consistency, Smoothness Classes, and Fast Rates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.15595","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":"sha256:152588a871538e9bc50afa52a144bbc3ec34dc3010a725a5594da18384df632a","target":"record","created_at":"2026-07-05T03:44:47Z","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":"1b7ee8aba4ec7246610d1def379bbde6eb70e0333e5435378b5e411d986b1dc0","cross_cats_sorted":["cs.LG","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2021-12-31T18:57:37Z","title_canon_sha256":"9b922826c2a5b3b7d4a6820766faac58806e5fdb098200b65b6e5971ea489afc"},"schema_version":"1.0","source":{"id":"2112.15595","kind":"arxiv","version":1}},"canonical_sha256":"3a9fe0776af147519b04b0dbe4098e3b123f3a7318d60d3681c9b5eb78ff3837","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a9fe0776af147519b04b0dbe4098e3b123f3a7318d60d3681c9b5eb78ff3837","first_computed_at":"2026-07-05T03:44:47.887391Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:44:47.887391Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GK2+Ug/t8ow9XK844Aat2HD7kNQPuG9yd2OIA7HQDX6di78fMDPjZAfc6YkdeWry6P1vfSjyru/2vONrW8jjAg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:44:47.887744Z","signed_message":"canonical_sha256_bytes"},"source_id":"2112.15595","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:152588a871538e9bc50afa52a144bbc3ec34dc3010a725a5594da18384df632a","sha256:18bb19b158b903a31052f8339aeee36a564869364ab2c72e4595c0594ab01299"],"state_sha256":"6f1e044b77eddc317fb39e219fa15781ebcc3187671e4b6934ab86cde6c7d74e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pdSCswh7upytolZuPuJ3b1Usoy6e2PV3u4CCp91UChdbU9T0C8onuFx+iwt9q2iyd3+2ruMSBGs39QW2gsWWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T15:19:58.665252Z","bundle_sha256":"adac4f6607063267ecd59340e77010a2a94d26863a3db4378524885f2ae3ffbe"}}