{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:5O4BALY7AYYRKVPGCPIXDGYYBU","short_pith_number":"pith:5O4BALY7","schema_version":"1.0","canonical_sha256":"ebb8102f1f06311555e613d1719b180d19c8c0e7ffaa20406467f45700c51a75","source":{"kind":"arxiv","id":"1906.04601","version":1},"attestation_state":"computed","paper":{"title":"A proof of the mean-field limit for $\\lambda$-convex potentials by $\\Gamma$-Convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"G. A. Pavliotis, J. A. Carrillo, M. G. Delgadino","submitted_at":"2019-06-11T13:52:16Z","abstract_excerpt":"In this work we give a proof of the mean-field limit for $\\lambda$-convex potentials using a purely variational viewpoint. Our approach is based on the observation that all evolution equations that we study can be written as gradient flows of functionals at different levels: in the set of probability measures, in the set of symmetric probability measures on $N$ variables, and in the set of probability measures on probability measures. This basic fact allows us to rely on $\\Gamma$-convergence tools for gradient flows to complete the proof by identifying the limits of the different terms in the "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1906.04601","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-11T13:52:16Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"414a70b60aa790bb7d4029d16d4e67b4e75d22154411571d8be4c50bd9ff314d","abstract_canon_sha256":"afa0f5c4693712e71d5e646290c7600a798e2447e32d53aa88891e7620448d6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:38.796029Z","signature_b64":"TlkVVheOzLFUR/ar6p/oxkOguypqTae0ItbmULbm1cHCQrBBIx2Q30D4xuqgXNbj6FZk389EKXg7w0tRsraSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebb8102f1f06311555e613d1719b180d19c8c0e7ffaa20406467f45700c51a75","last_reissued_at":"2026-05-17T23:43:38.795534Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:38.795534Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A proof of the mean-field limit for $\\lambda$-convex potentials by $\\Gamma$-Convergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"G. A. Pavliotis, J. A. Carrillo, M. G. Delgadino","submitted_at":"2019-06-11T13:52:16Z","abstract_excerpt":"In this work we give a proof of the mean-field limit for $\\lambda$-convex potentials using a purely variational viewpoint. Our approach is based on the observation that all evolution equations that we study can be written as gradient flows of functionals at different levels: in the set of probability measures, in the set of symmetric probability measures on $N$ variables, and in the set of probability measures on probability measures. This basic fact allows us to rely on $\\Gamma$-convergence tools for gradient flows to complete the proof by identifying the limits of the different terms in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04601","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1906.04601","created_at":"2026-05-17T23:43:38.795609+00:00"},{"alias_kind":"arxiv_version","alias_value":"1906.04601v1","created_at":"2026-05-17T23:43:38.795609+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04601","created_at":"2026-05-17T23:43:38.795609+00:00"},{"alias_kind":"pith_short_12","alias_value":"5O4BALY7AYYR","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_16","alias_value":"5O4BALY7AYYRKVPG","created_at":"2026-05-18T12:33:10.108867+00:00"},{"alias_kind":"pith_short_8","alias_value":"5O4BALY7","created_at":"2026-05-18T12:33:10.108867+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5O4BALY7AYYRKVPGCPIXDGYYBU","json":"https://pith.science/pith/5O4BALY7AYYRKVPGCPIXDGYYBU.json","graph_json":"https://pith.science/api/pith-number/5O4BALY7AYYRKVPGCPIXDGYYBU/graph.json","events_json":"https://pith.science/api/pith-number/5O4BALY7AYYRKVPGCPIXDGYYBU/events.json","paper":"https://pith.science/paper/5O4BALY7"},"agent_actions":{"view_html":"https://pith.science/pith/5O4BALY7AYYRKVPGCPIXDGYYBU","download_json":"https://pith.science/pith/5O4BALY7AYYRKVPGCPIXDGYYBU.json","view_paper":"https://pith.science/paper/5O4BALY7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1906.04601&json=true","fetch_graph":"https://pith.science/api/pith-number/5O4BALY7AYYRKVPGCPIXDGYYBU/graph.json","fetch_events":"https://pith.science/api/pith-number/5O4BALY7AYYRKVPGCPIXDGYYBU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5O4BALY7AYYRKVPGCPIXDGYYBU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5O4BALY7AYYRKVPGCPIXDGYYBU/action/storage_attestation","attest_author":"https://pith.science/pith/5O4BALY7AYYRKVPGCPIXDGYYBU/action/author_attestation","sign_citation":"https://pith.science/pith/5O4BALY7AYYRKVPGCPIXDGYYBU/action/citation_signature","submit_replication":"https://pith.science/pith/5O4BALY7AYYRKVPGCPIXDGYYBU/action/replication_record"}},"created_at":"2026-05-17T23:43:38.795609+00:00","updated_at":"2026-05-17T23:43:38.795609+00:00"}