{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LOVRI2V2PA23CBDFRGJXNOVDV2","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":"95890dea567e71b07c581041ed079f846ddbf2d2999c8affa98690b5ca5a1427","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-07-14T19:26:32Z","title_canon_sha256":"e53d3b076cdaeea73fc26ad707adc6b07b3081ce7bcbf72ec76372aaa6b06086"},"schema_version":"1.0","source":{"id":"2307.07587","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.07587","created_at":"2026-07-05T06:30:59Z"},{"alias_kind":"arxiv_version","alias_value":"2307.07587v1","created_at":"2026-07-05T06:30:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.07587","created_at":"2026-07-05T06:30:59Z"},{"alias_kind":"pith_short_12","alias_value":"LOVRI2V2PA23","created_at":"2026-07-05T06:30:59Z"},{"alias_kind":"pith_short_16","alias_value":"LOVRI2V2PA23CBDF","created_at":"2026-07-05T06:30:59Z"},{"alias_kind":"pith_short_8","alias_value":"LOVRI2V2","created_at":"2026-07-05T06:30:59Z"}],"graph_snapshots":[{"event_id":"sha256:ab69cab87381d7c0a7c10aa92046835b14ac4bb546721cd7c72419b826137fa3","target":"graph","created_at":"2026-07-05T06:30:59Z","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/2307.07587/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider mean-field limits for overdamped Langevin dynamics of $N$ particles with possibly singular interactions. It has been shown that a modulated free energy method can be used to prove the mean-field convergence or propagation of chaos for a certain class of interactions, including Riesz kernels. We show here that generation of chaos, i.e. exponential-in-time convergence to a tensorized (or iid) state starting from a nontensorized one, can be deduced from the modulated free energy method provided a uniform-in-$N$ \"modulated logarithmic Sobolev inequality\" holds. Proving such an inequali","authors_text":"Matthew Rosenzweig, Sylvia Serfaty","cross_cats":["math-ph","math.AP","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-07-14T19:26:32Z","title":"Modulated logarithmic Sobolev inequalities and generation of chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.07587","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":"sha256:49f1aed82eece426b1db7b8a74bfbb79e9e07d07771cf0b4bc99fa2dfe667096","target":"record","created_at":"2026-07-05T06:30:59Z","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":"95890dea567e71b07c581041ed079f846ddbf2d2999c8affa98690b5ca5a1427","cross_cats_sorted":["math-ph","math.AP","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2023-07-14T19:26:32Z","title_canon_sha256":"e53d3b076cdaeea73fc26ad707adc6b07b3081ce7bcbf72ec76372aaa6b06086"},"schema_version":"1.0","source":{"id":"2307.07587","kind":"arxiv","version":1}},"canonical_sha256":"5bab146aba7835b10465899376baa3ae8677da740d67bd9a5b67d88ff8d1accc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5bab146aba7835b10465899376baa3ae8677da740d67bd9a5b67d88ff8d1accc","first_computed_at":"2026-07-05T06:30:59.307102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:30:59.307102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KQVndN7amvuzQ4eOmRCwE3I7VGV0tTxFaYFpfvvmxmLep8B7LZAUJZgTcTNqKrDl4UYmeFM/EMn5FWC+NeOFDg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:30:59.307584Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.07587","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49f1aed82eece426b1db7b8a74bfbb79e9e07d07771cf0b4bc99fa2dfe667096","sha256:ab69cab87381d7c0a7c10aa92046835b14ac4bb546721cd7c72419b826137fa3"],"state_sha256":"037b370927dd753cdc5f56cac3ec1e8a5c6144df6cd5e2896ee23be70c71e204"}