{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:QPA2B22OTHS2CPVTS4U63VRUWU","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":"cf99797a73fc25e252bf227f572fa4c3fe0a53630ce5788686d9c8fb5d36c839","cross_cats_sorted":["cs.LG","math.FA","stat.CO","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2020-09-22T03:41:45Z","title_canon_sha256":"7294dfc893d2f99283ca1ff12d2202667988dbb835cc8f167cf2b5c4a3fc88a4"},"schema_version":"1.0","source":{"id":"2009.10303","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.10303","created_at":"2026-07-05T07:48:42Z"},{"alias_kind":"arxiv_version","alias_value":"2009.10303v3","created_at":"2026-07-05T07:48:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.10303","created_at":"2026-07-05T07:48:42Z"},{"alias_kind":"pith_short_12","alias_value":"QPA2B22OTHS2","created_at":"2026-07-05T07:48:42Z"},{"alias_kind":"pith_short_16","alias_value":"QPA2B22OTHS2CPVT","created_at":"2026-07-05T07:48:42Z"},{"alias_kind":"pith_short_8","alias_value":"QPA2B22O","created_at":"2026-07-05T07:48:42Z"}],"graph_snapshots":[{"event_id":"sha256:76b1a68317ba2b8d059ad270600b7f29fc7bfc0b04e524f8985fb36969dcf1db","target":"graph","created_at":"2026-07-05T07:48:42Z","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/2009.10303/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Transportation of measure provides a versatile approach for modeling complex probability distributions, with applications in density estimation, Bayesian inference, generative modeling, and beyond. Monotone triangular transport maps$\\unicode{x2014}$approximations of the Knothe$\\unicode{x2013}$Rosenblatt (KR) rearrangement$\\unicode{x2014}$are a canonical choice for these tasks. Yet the representation and parameterization of such maps have a significant impact on their generality and expressiveness, and on properties of the optimization problem that arises in learning a map from data (e.g., via ","authors_text":"Olivier Zahm, Ricardo Baptista, Youssef Marzouk","cross_cats":["cs.LG","math.FA","stat.CO","stat.ME"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2020-09-22T03:41:45Z","title":"On the representation and learning of monotone triangular transport maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.10303","kind":"arxiv","version":3},"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":"sha256:2ee5b48f204469a6ca8d9e6508228d1dcd4c225d570abeb54d36abc2fc5acb49","target":"record","created_at":"2026-07-05T07:48:42Z","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":"cf99797a73fc25e252bf227f572fa4c3fe0a53630ce5788686d9c8fb5d36c839","cross_cats_sorted":["cs.LG","math.FA","stat.CO","stat.ME"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2020-09-22T03:41:45Z","title_canon_sha256":"7294dfc893d2f99283ca1ff12d2202667988dbb835cc8f167cf2b5c4a3fc88a4"},"schema_version":"1.0","source":{"id":"2009.10303","kind":"arxiv","version":3}},"canonical_sha256":"83c1a0eb4e99e5a13eb39729edd634b52012d70b391a1b7c6b1a78daea7cecca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83c1a0eb4e99e5a13eb39729edd634b52012d70b391a1b7c6b1a78daea7cecca","first_computed_at":"2026-07-05T07:48:42.401253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:48:42.401253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pI/BLvmqG7/udzYvLYA194dpHoHxvSVThnyw/fmxl2+U3nyhM3m3Pfle4zwzay+dH6BU7opL81AnaFVuCnW9Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T07:48:42.401660Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.10303","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ee5b48f204469a6ca8d9e6508228d1dcd4c225d570abeb54d36abc2fc5acb49","sha256:76b1a68317ba2b8d059ad270600b7f29fc7bfc0b04e524f8985fb36969dcf1db"],"state_sha256":"8c5ed410554ba87f1bd98201bbc0b5c091b2373c3afbc7f8a47ff42b3a41a173"}