{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:R2PIITV6V64NB6R4GT63BJ6BT4","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":"517dac58dea39770f4dff200411814bc6e693750473566225b261af709014526","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-03-04T04:56:23Z","title_canon_sha256":"d2ed2b5ef10777e43cb1c8de3dbfa18a8373987317d8a2276983e8d463ab1df2"},"schema_version":"1.0","source":{"id":"2503.02276","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.02276","created_at":"2026-07-05T10:24:33Z"},{"alias_kind":"arxiv_version","alias_value":"2503.02276v2","created_at":"2026-07-05T10:24:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.02276","created_at":"2026-07-05T10:24:33Z"},{"alias_kind":"pith_short_12","alias_value":"R2PIITV6V64N","created_at":"2026-07-05T10:24:33Z"},{"alias_kind":"pith_short_16","alias_value":"R2PIITV6V64NB6R4","created_at":"2026-07-05T10:24:33Z"},{"alias_kind":"pith_short_8","alias_value":"R2PIITV6","created_at":"2026-07-05T10:24:33Z"}],"graph_snapshots":[{"event_id":"sha256:860de798272b27f42bd191f478dbfc52fe4f80c6f60952e48abc7b4c7d45bf3b","target":"graph","created_at":"2026-07-05T10:24:33Z","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/2503.02276/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the mean field limit for singular dynamics with time evolving weights. Our results are an extension of the work of Serfaty \\cite{duerinckx2020mean} and Bresch-Jabin-Wang \\cite{bresch2019modulated}, which consider singular Coulomb flows with weights which are constant time. The inclusion of time dependent weights necessitates the commutator estimates of \\cite{duerinckx2020mean,bresch2019modulated}, as well as a new functional inequality. The well-posedness of the mean field PDE and the associated system of trajectories is also proved.","authors_text":"Immanuel Ben Porat, Jos\\'e A. Carrillo, Pierre-Emmanuel Jabin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-03-04T04:56:23Z","title":"Singular flows with time-varying weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.02276","kind":"arxiv","version":2},"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":"sha256:4c961f72dbb30bab30a00240020f6d0ef3da61a4c83eb53fe0a9c8ed58db6b94","target":"record","created_at":"2026-07-05T10:24:33Z","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":"517dac58dea39770f4dff200411814bc6e693750473566225b261af709014526","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2025-03-04T04:56:23Z","title_canon_sha256":"d2ed2b5ef10777e43cb1c8de3dbfa18a8373987317d8a2276983e8d463ab1df2"},"schema_version":"1.0","source":{"id":"2503.02276","kind":"arxiv","version":2}},"canonical_sha256":"8e9e844ebeafb8d0fa3c34fdb0a7c19f02aaa520f6735135e4c32941c57ca8e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e9e844ebeafb8d0fa3c34fdb0a7c19f02aaa520f6735135e4c32941c57ca8e0","first_computed_at":"2026-07-05T10:24:33.061666Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:24:33.061666Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"it4UXWjMj3YJctVR50O1I7l1zViveFmW1M6Mw8xpzP19y1myIdes0b6wHikxc2sH8mPbQVNmL9QBM5WqBagQBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:24:33.062172Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.02276","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c961f72dbb30bab30a00240020f6d0ef3da61a4c83eb53fe0a9c8ed58db6b94","sha256:860de798272b27f42bd191f478dbfc52fe4f80c6f60952e48abc7b4c7d45bf3b"],"state_sha256":"3e14230970c87f9bb6e1483c5518af8b47818eba513f4f99924726d8d59c577a"}