{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:KBXEGSJHAQFUCOQDXD5C5COI2R","short_pith_number":"pith:KBXEGSJH","canonical_record":{"source":{"id":"2006.00702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-06-01T04:06:38Z","cross_cats_sorted":["math.DS","math.PR","physics.data-an","stat.ME"],"title_canon_sha256":"7b106fa94114133538fe2ef2af65ef67ec5fdb0df953752063e7caae0d7dd91d","abstract_canon_sha256":"cf849a347f737dc6a3bde5cd965a588e7c859d97d890bc81f28da998182ef866"},"schema_version":"1.0"},"canonical_sha256":"506e434927040b413a03b8fa2e89c8d4433ee61bbd65d8949fca619c3b91c773","source":{"kind":"arxiv","id":"2006.00702","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.00702","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"arxiv_version","alias_value":"2006.00702v1","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.00702","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"pith_short_12","alias_value":"KBXEGSJHAQFU","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"pith_short_16","alias_value":"KBXEGSJHAQFUCOQD","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"pith_short_8","alias_value":"KBXEGSJH","created_at":"2026-07-05T01:30:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:KBXEGSJHAQFUCOQDXD5C5COI2R","target":"record","payload":{"canonical_record":{"source":{"id":"2006.00702","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-06-01T04:06:38Z","cross_cats_sorted":["math.DS","math.PR","physics.data-an","stat.ME"],"title_canon_sha256":"7b106fa94114133538fe2ef2af65ef67ec5fdb0df953752063e7caae0d7dd91d","abstract_canon_sha256":"cf849a347f737dc6a3bde5cd965a588e7c859d97d890bc81f28da998182ef866"},"schema_version":"1.0"},"canonical_sha256":"506e434927040b413a03b8fa2e89c8d4433ee61bbd65d8949fca619c3b91c773","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:30:05.133141Z","signature_b64":"szVW7kESIiIDvhGw9ZPukwXtNaZaioyq7l9/VP5NdfRv38uZGVwBDyAcFImQSn4MLh3/f9dtFtfu8h9TVdUCDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"506e434927040b413a03b8fa2e89c8d4433ee61bbd65d8949fca619c3b91c773","last_reissued_at":"2026-07-05T01:30:05.132762Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:30:05.132762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2006.00702","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":"2026-07-05T01:30:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PeKAlKAQlBC6cR+Sme2SRwqX2NooELjzvrik4naMskNUaE1XexV+OFVz1hKX5MPtbkwZ0RQLBBENx1aE8qwsCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:08:38.341653Z"},"content_sha256":"52a6b8274eac6eae60550297b018e2faf3cf2114567e44f2beb5d1f96f6d48ca","schema_version":"1.0","event_id":"sha256:52a6b8274eac6eae60550297b018e2faf3cf2114567e44f2beb5d1f96f6d48ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:KBXEGSJHAQFUCOQDXD5C5COI2R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.PR","physics.data-an","stat.ME"],"primary_cat":"cond-mat.stat-mech","authors_text":"Dimitra Maoutsa, Manfred Opper, Sebastian Reich","submitted_at":"2020-06-01T04:06:38Z","abstract_excerpt":"Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker-Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.00702","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/2006.00702/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":"2026-07-05T01:30:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j/1oNaYuaPvALCnOa1pt494sZHa3ppYdEmuBCZmcgmEfvlGsT/360wS9EIugKUpA6UgMlJsg9U9vxBvYXCYDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T15:08:38.342453Z"},"content_sha256":"7d9c81e1363066bd20e1dc66e127f772627e93385567bedd73a49dd93841ddab","schema_version":"1.0","event_id":"sha256:7d9c81e1363066bd20e1dc66e127f772627e93385567bedd73a49dd93841ddab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KBXEGSJHAQFUCOQDXD5C5COI2R/bundle.json","state_url":"https://pith.science/pith/KBXEGSJHAQFUCOQDXD5C5COI2R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KBXEGSJHAQFUCOQDXD5C5COI2R/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":"2026-08-16T15:08:38Z","links":{"resolver":"https://pith.science/pith/KBXEGSJHAQFUCOQDXD5C5COI2R","bundle":"https://pith.science/pith/KBXEGSJHAQFUCOQDXD5C5COI2R/bundle.json","state":"https://pith.science/pith/KBXEGSJHAQFUCOQDXD5C5COI2R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KBXEGSJHAQFUCOQDXD5C5COI2R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:KBXEGSJHAQFUCOQDXD5C5COI2R","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":"cf849a347f737dc6a3bde5cd965a588e7c859d97d890bc81f28da998182ef866","cross_cats_sorted":["math.DS","math.PR","physics.data-an","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-06-01T04:06:38Z","title_canon_sha256":"7b106fa94114133538fe2ef2af65ef67ec5fdb0df953752063e7caae0d7dd91d"},"schema_version":"1.0","source":{"id":"2006.00702","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2006.00702","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"arxiv_version","alias_value":"2006.00702v1","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.00702","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"pith_short_12","alias_value":"KBXEGSJHAQFU","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"pith_short_16","alias_value":"KBXEGSJHAQFUCOQD","created_at":"2026-07-05T01:30:05Z"},{"alias_kind":"pith_short_8","alias_value":"KBXEGSJH","created_at":"2026-07-05T01:30:05Z"}],"graph_snapshots":[{"event_id":"sha256:7d9c81e1363066bd20e1dc66e127f772627e93385567bedd73a49dd93841ddab","target":"graph","created_at":"2026-07-05T01:30:05Z","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/2006.00702/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment only in limited settings, and often is inevitable to resort to numerical solutions. Here, we develop a computational approach for simulating the time evolution of Fokker-Planck solutions in terms of a mean field limit of an interacting particle system. The interactions between particles are determined by the gradient of the logarithm of the particle density","authors_text":"Dimitra Maoutsa, Manfred Opper, Sebastian Reich","cross_cats":["math.DS","math.PR","physics.data-an","stat.ME"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-06-01T04:06:38Z","title":"Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.00702","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":"sha256:52a6b8274eac6eae60550297b018e2faf3cf2114567e44f2beb5d1f96f6d48ca","target":"record","created_at":"2026-07-05T01:30:05Z","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":"cf849a347f737dc6a3bde5cd965a588e7c859d97d890bc81f28da998182ef866","cross_cats_sorted":["math.DS","math.PR","physics.data-an","stat.ME"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2020-06-01T04:06:38Z","title_canon_sha256":"7b106fa94114133538fe2ef2af65ef67ec5fdb0df953752063e7caae0d7dd91d"},"schema_version":"1.0","source":{"id":"2006.00702","kind":"arxiv","version":1}},"canonical_sha256":"506e434927040b413a03b8fa2e89c8d4433ee61bbd65d8949fca619c3b91c773","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"506e434927040b413a03b8fa2e89c8d4433ee61bbd65d8949fca619c3b91c773","first_computed_at":"2026-07-05T01:30:05.132762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:30:05.132762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"szVW7kESIiIDvhGw9ZPukwXtNaZaioyq7l9/VP5NdfRv38uZGVwBDyAcFImQSn4MLh3/f9dtFtfu8h9TVdUCDw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:30:05.133141Z","signed_message":"canonical_sha256_bytes"},"source_id":"2006.00702","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52a6b8274eac6eae60550297b018e2faf3cf2114567e44f2beb5d1f96f6d48ca","sha256:7d9c81e1363066bd20e1dc66e127f772627e93385567bedd73a49dd93841ddab"],"state_sha256":"0ae613fdf3bb87d411be712882b3cae8d12b1fd07d76d56f80c6cbf9330da53f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O7rFSHqwX1wSWNHlWYDwVkp1NjsMoMUfmlvIJVERtf8ShQOfGmZMWXNBx4Ao2Hh9ALPHAXxUEWA4JMNKrEUUDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T15:08:38.348384Z","bundle_sha256":"96617705c72e02f323cb98aebb84b5269b5cc9f2fbeffd29c6bd5d0ff6de0d82"}}