{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:W7XXV4WF6LKDIW44BVVIKGZWPQ","short_pith_number":"pith:W7XXV4WF","canonical_record":{"source":{"id":"2203.15747","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-29T16:56:32Z","cross_cats_sorted":[],"title_canon_sha256":"2eda3b16fbb0c584946e6a2505a81df6fe9ff8c4541f97d1ef62b1af67369dfe","abstract_canon_sha256":"8e03f234186038ad2b29db0006f55b97aaab29da87efff99012f7ee026b816fd"},"schema_version":"1.0"},"canonical_sha256":"b7ef7af2c5f2d4345b9c0d6a851b367c1f65c186a1ed0aefe1413f9db83d2af5","source":{"kind":"arxiv","id":"2203.15747","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.15747","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"arxiv_version","alias_value":"2203.15747v4","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.15747","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"pith_short_12","alias_value":"W7XXV4WF6LKD","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"pith_short_16","alias_value":"W7XXV4WF6LKDIW44","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"pith_short_8","alias_value":"W7XXV4WF","created_at":"2026-07-05T10:42:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:W7XXV4WF6LKDIW44BVVIKGZWPQ","target":"record","payload":{"canonical_record":{"source":{"id":"2203.15747","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-29T16:56:32Z","cross_cats_sorted":[],"title_canon_sha256":"2eda3b16fbb0c584946e6a2505a81df6fe9ff8c4541f97d1ef62b1af67369dfe","abstract_canon_sha256":"8e03f234186038ad2b29db0006f55b97aaab29da87efff99012f7ee026b816fd"},"schema_version":"1.0"},"canonical_sha256":"b7ef7af2c5f2d4345b9c0d6a851b367c1f65c186a1ed0aefe1413f9db83d2af5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:42:32.640909Z","signature_b64":"mOZsBwskHxo2swaOXt5OGJIOFukxJGCaEYbBYIaPzMmIL0idhv5rc82wpEGW7G/mmmsA9idSysY9TiMpRpZrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7ef7af2c5f2d4345b9c0d6a851b367c1f65c186a1ed0aefe1413f9db83d2af5","last_reissued_at":"2026-07-05T10:42:32.640440Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:42:32.640440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2203.15747","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:42:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ll250QTUBzv8jzqgXybF8T6azF5LhYFeCKMoDk97XXsnEHBELCuMQSRycnFiCGi8whFDr/JLQu+yU+Zj45TzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:12:23.067303Z"},"content_sha256":"fd8a67c4716672b69b19d84d86235978476ab525978599f128f4ac866f3fc965","schema_version":"1.0","event_id":"sha256:fd8a67c4716672b69b19d84d86235978476ab525978599f128f4ac866f3fc965"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:W7XXV4WF6LKDIW44BVVIKGZWPQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new approach to the mean-field limit of Vlasov-Fokker-Planck equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Didier Bresch, Juan Soler, Pierre-Emmanuel Jabin","submitted_at":"2022-03-29T16:56:32Z","abstract_excerpt":"This article introduces a novel approach to the mean-field limit of stochastic systems of interacting particles, leading to the first ever derivation of the mean-field limit to the Vlasov-Poisson-Fokker-Planck system for plasmas in dimension~$2$ together with a partial result in dimension~$3$. The method is broadly compatible with second order systems that lead to kinetic equations and it relies on novel estimates on the BBGKY hierarchy. By taking advantage of the diffusion in velocity, those estimates bound weighted $L^p$ norms of the marginals or observables of the system, uniformly in the n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.15747","kind":"arxiv","version":4},"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/2203.15747/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":"2026-07-05T10:42:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d124D1PNAUnL2z1PJR/42sy69ybomon2hdedoxFG/idVVUBeDnh3XGHi2n1FcDkZP3BpxSykwMQwHomZYc2TAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T13:12:23.067797Z"},"content_sha256":"82205a9653ee0115766239b09756bbf7a6da8edc980d9bcfd00f8061e16d3a20","schema_version":"1.0","event_id":"sha256:82205a9653ee0115766239b09756bbf7a6da8edc980d9bcfd00f8061e16d3a20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W7XXV4WF6LKDIW44BVVIKGZWPQ/bundle.json","state_url":"https://pith.science/pith/W7XXV4WF6LKDIW44BVVIKGZWPQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W7XXV4WF6LKDIW44BVVIKGZWPQ/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":"2026-08-09T13:12:23Z","links":{"resolver":"https://pith.science/pith/W7XXV4WF6LKDIW44BVVIKGZWPQ","bundle":"https://pith.science/pith/W7XXV4WF6LKDIW44BVVIKGZWPQ/bundle.json","state":"https://pith.science/pith/W7XXV4WF6LKDIW44BVVIKGZWPQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W7XXV4WF6LKDIW44BVVIKGZWPQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:W7XXV4WF6LKDIW44BVVIKGZWPQ","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":"8e03f234186038ad2b29db0006f55b97aaab29da87efff99012f7ee026b816fd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-29T16:56:32Z","title_canon_sha256":"2eda3b16fbb0c584946e6a2505a81df6fe9ff8c4541f97d1ef62b1af67369dfe"},"schema_version":"1.0","source":{"id":"2203.15747","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2203.15747","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"arxiv_version","alias_value":"2203.15747v4","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2203.15747","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"pith_short_12","alias_value":"W7XXV4WF6LKD","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"pith_short_16","alias_value":"W7XXV4WF6LKDIW44","created_at":"2026-07-05T10:42:32Z"},{"alias_kind":"pith_short_8","alias_value":"W7XXV4WF","created_at":"2026-07-05T10:42:32Z"}],"graph_snapshots":[{"event_id":"sha256:82205a9653ee0115766239b09756bbf7a6da8edc980d9bcfd00f8061e16d3a20","target":"graph","created_at":"2026-07-05T10:42:32Z","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/2203.15747/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This article introduces a novel approach to the mean-field limit of stochastic systems of interacting particles, leading to the first ever derivation of the mean-field limit to the Vlasov-Poisson-Fokker-Planck system for plasmas in dimension~$2$ together with a partial result in dimension~$3$. The method is broadly compatible with second order systems that lead to kinetic equations and it relies on novel estimates on the BBGKY hierarchy. By taking advantage of the diffusion in velocity, those estimates bound weighted $L^p$ norms of the marginals or observables of the system, uniformly in the n","authors_text":"Didier Bresch, Juan Soler, Pierre-Emmanuel Jabin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-29T16:56:32Z","title":"A new approach to the mean-field limit of Vlasov-Fokker-Planck equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2203.15747","kind":"arxiv","version":4},"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:fd8a67c4716672b69b19d84d86235978476ab525978599f128f4ac866f3fc965","target":"record","created_at":"2026-07-05T10:42:32Z","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":"8e03f234186038ad2b29db0006f55b97aaab29da87efff99012f7ee026b816fd","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-03-29T16:56:32Z","title_canon_sha256":"2eda3b16fbb0c584946e6a2505a81df6fe9ff8c4541f97d1ef62b1af67369dfe"},"schema_version":"1.0","source":{"id":"2203.15747","kind":"arxiv","version":4}},"canonical_sha256":"b7ef7af2c5f2d4345b9c0d6a851b367c1f65c186a1ed0aefe1413f9db83d2af5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b7ef7af2c5f2d4345b9c0d6a851b367c1f65c186a1ed0aefe1413f9db83d2af5","first_computed_at":"2026-07-05T10:42:32.640440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:42:32.640440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mOZsBwskHxo2swaOXt5OGJIOFukxJGCaEYbBYIaPzMmIL0idhv5rc82wpEGW7G/mmmsA9idSysY9TiMpRpZrAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:42:32.640909Z","signed_message":"canonical_sha256_bytes"},"source_id":"2203.15747","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd8a67c4716672b69b19d84d86235978476ab525978599f128f4ac866f3fc965","sha256:82205a9653ee0115766239b09756bbf7a6da8edc980d9bcfd00f8061e16d3a20"],"state_sha256":"154096ecf1d0f95124627c2f09806face173e0c5c2094ef047381bf9a0b1f71a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2XFNQjOXVGO6bY1MZQ7q3+pIkah6LJsTEFvWEz7T0n9Rf63LU6lnDxVTwPa92e713veMM5T6uIngYPwMCO5Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T13:12:23.071520Z","bundle_sha256":"a0b12af333cd750f06fb824d3c3f329b1228951c02155b876d480e0a94412380"}}