{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:YNBM5TXWTCRLBGWERRJ6DEVFGB","short_pith_number":"pith:YNBM5TXW","canonical_record":{"source":{"id":"2411.12430","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-19T11:40:56Z","cross_cats_sorted":["cs.NA","math.OC"],"title_canon_sha256":"ba2090d9be9c0fe3720f9815238fbc35ba4f6254de1d40ec16d64e4009937230","abstract_canon_sha256":"b7e44ebfb31d2eded70d85b77008d647af6c1b800a2d7b651fe0546f97074b3b"},"schema_version":"1.0"},"canonical_sha256":"c342cecef698a2b09ac48c53e192a5306e2f3b4de80b9d06fcff79b7b63890c8","source":{"kind":"arxiv","id":"2411.12430","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.12430","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"arxiv_version","alias_value":"2411.12430v1","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12430","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"pith_short_12","alias_value":"YNBM5TXWTCRL","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"pith_short_16","alias_value":"YNBM5TXWTCRLBGWE","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"pith_short_8","alias_value":"YNBM5TXW","created_at":"2026-07-05T09:37:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:YNBM5TXWTCRLBGWERRJ6DEVFGB","target":"record","payload":{"canonical_record":{"source":{"id":"2411.12430","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-19T11:40:56Z","cross_cats_sorted":["cs.NA","math.OC"],"title_canon_sha256":"ba2090d9be9c0fe3720f9815238fbc35ba4f6254de1d40ec16d64e4009937230","abstract_canon_sha256":"b7e44ebfb31d2eded70d85b77008d647af6c1b800a2d7b651fe0546f97074b3b"},"schema_version":"1.0"},"canonical_sha256":"c342cecef698a2b09ac48c53e192a5306e2f3b4de80b9d06fcff79b7b63890c8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:37:21.714271Z","signature_b64":"aLvCFIIIAFstftTLj8BAPUvFfKKUn747uWH1rl7QmJOZsgQZyBmRbu3AR5hSy9T2UyWytcCqYPnsQE+xxwllAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c342cecef698a2b09ac48c53e192a5306e2f3b4de80b9d06fcff79b7b63890c8","last_reissued_at":"2026-07-05T09:37:21.713726Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:37:21.713726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.12430","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":"2026-07-05T09:37:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ar+XoKSpYv6DBzgsLfYAXTw6xbiy+JXYQrD9+mWw+Dlj1xUApqTPXZJYzIJINKV68X/1IF5shBR6C0H2BfC9DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:59:15.926040Z"},"content_sha256":"f377538d595449c2ca0b0c585673d71797cc1e3546723d71a7344b851dc62e4a","schema_version":"1.0","event_id":"sha256:f377538d595449c2ca0b0c585673d71797cc1e3546723d71a7344b851dc62e4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:YNBM5TXWTCRLBGWERRJ6DEVFGB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Eulerian approach to regularized JKO scheme with low-rank tensor decompositions for Bayesian inversion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Martin Eigel, Vitalii Aksenov","submitted_at":"2024-11-19T11:40:56Z","abstract_excerpt":"The possibility of using the Eulerian discretization for the problem of modelling high-dimensional distributions and sampling, is studied. The problem is posed as a minimization problem over the space of probability measures with respect to the Wasserstein distance and solved with entropy-regularized JKO scheme. Each proximal step can be formulated as a fixed-point equation and solved with accelerated methods, such as Anderson's. The usage of low-rank Tensor Train format allows to overcome the \\emph{curse of dimensionality}, i.e. the exponential growth of degrees of freedom with dimension, inh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12430","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/2411.12430/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":"2026-07-05T09:37:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fUA2TGC06ocEPDLMwNj4ZyM/M9YM1wUKS6hr14n4OHM72/R0nPq837kVu3k9Luiw+YqkWpqhqAXXeHi+e4ISAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T08:59:15.926552Z"},"content_sha256":"9deb85e5ac511abe7f3b072cf4987332a550fc92b10d553e1fde3bb058108444","schema_version":"1.0","event_id":"sha256:9deb85e5ac511abe7f3b072cf4987332a550fc92b10d553e1fde3bb058108444"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YNBM5TXWTCRLBGWERRJ6DEVFGB/bundle.json","state_url":"https://pith.science/pith/YNBM5TXWTCRLBGWERRJ6DEVFGB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YNBM5TXWTCRLBGWERRJ6DEVFGB/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":"2026-08-13T08:59:15Z","links":{"resolver":"https://pith.science/pith/YNBM5TXWTCRLBGWERRJ6DEVFGB","bundle":"https://pith.science/pith/YNBM5TXWTCRLBGWERRJ6DEVFGB/bundle.json","state":"https://pith.science/pith/YNBM5TXWTCRLBGWERRJ6DEVFGB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YNBM5TXWTCRLBGWERRJ6DEVFGB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:YNBM5TXWTCRLBGWERRJ6DEVFGB","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":"b7e44ebfb31d2eded70d85b77008d647af6c1b800a2d7b651fe0546f97074b3b","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-19T11:40:56Z","title_canon_sha256":"ba2090d9be9c0fe3720f9815238fbc35ba4f6254de1d40ec16d64e4009937230"},"schema_version":"1.0","source":{"id":"2411.12430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.12430","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"arxiv_version","alias_value":"2411.12430v1","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.12430","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"pith_short_12","alias_value":"YNBM5TXWTCRL","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"pith_short_16","alias_value":"YNBM5TXWTCRLBGWE","created_at":"2026-07-05T09:37:21Z"},{"alias_kind":"pith_short_8","alias_value":"YNBM5TXW","created_at":"2026-07-05T09:37:21Z"}],"graph_snapshots":[{"event_id":"sha256:9deb85e5ac511abe7f3b072cf4987332a550fc92b10d553e1fde3bb058108444","target":"graph","created_at":"2026-07-05T09:37:21Z","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/2411.12430/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The possibility of using the Eulerian discretization for the problem of modelling high-dimensional distributions and sampling, is studied. The problem is posed as a minimization problem over the space of probability measures with respect to the Wasserstein distance and solved with entropy-regularized JKO scheme. Each proximal step can be formulated as a fixed-point equation and solved with accelerated methods, such as Anderson's. The usage of low-rank Tensor Train format allows to overcome the \\emph{curse of dimensionality}, i.e. the exponential growth of degrees of freedom with dimension, inh","authors_text":"Martin Eigel, Vitalii Aksenov","cross_cats":["cs.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-19T11:40:56Z","title":"An Eulerian approach to regularized JKO scheme with low-rank tensor decompositions for Bayesian inversion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.12430","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:f377538d595449c2ca0b0c585673d71797cc1e3546723d71a7344b851dc62e4a","target":"record","created_at":"2026-07-05T09:37:21Z","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":"b7e44ebfb31d2eded70d85b77008d647af6c1b800a2d7b651fe0546f97074b3b","cross_cats_sorted":["cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2024-11-19T11:40:56Z","title_canon_sha256":"ba2090d9be9c0fe3720f9815238fbc35ba4f6254de1d40ec16d64e4009937230"},"schema_version":"1.0","source":{"id":"2411.12430","kind":"arxiv","version":1}},"canonical_sha256":"c342cecef698a2b09ac48c53e192a5306e2f3b4de80b9d06fcff79b7b63890c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c342cecef698a2b09ac48c53e192a5306e2f3b4de80b9d06fcff79b7b63890c8","first_computed_at":"2026-07-05T09:37:21.713726Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:37:21.713726Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aLvCFIIIAFstftTLj8BAPUvFfKKUn747uWH1rl7QmJOZsgQZyBmRbu3AR5hSy9T2UyWytcCqYPnsQE+xxwllAw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:37:21.714271Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.12430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f377538d595449c2ca0b0c585673d71797cc1e3546723d71a7344b851dc62e4a","sha256:9deb85e5ac511abe7f3b072cf4987332a550fc92b10d553e1fde3bb058108444"],"state_sha256":"874838fb3e1afd75217e804471f00dfd4585bd559f5b15c400fbc27e59b29d19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"shLA9+eNGocvm8wCDFKNEFooHvVjiyEhBeGEiqH5jjoqSC71qJDeCZ8jDB9oVBKbjqvgbB/i+G9D/Mj71dzgBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T08:59:15.931740Z","bundle_sha256":"a2e9f2b25d0f0f0128c96ed471b640df5c53e4d0471b0f985e577d2b9cb2fef9"}}