{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DQDXACYUUTO6NMEE4UAEL4LXLF","short_pith_number":"pith:DQDXACYU","schema_version":"1.0","canonical_sha256":"1c07700b14a4dde6b084e50045f1775974470e21b5076b28d351eaf02ae994e6","source":{"kind":"arxiv","id":"1307.2999","version":2},"attestation_state":"computed","paper":{"title":"On Mean Field Limits for Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Niklas Boers, Peter Pickl","submitted_at":"2013-07-11T07:30:09Z","abstract_excerpt":"We present a purely probabilistic proof of propagation of molecular chaos for $N$-particle systems in dimension $3$ with interaction forces scaling like $1/\\vert q\\vert^{\\lambda}$ with $\\lambda<2$ and cut-off at $q = N^{-1/3}$. The proof yields a Gronwall estimate for the maximal distance between exact microscopic and approximate mean-field dynamics. This can be used to show propagation of molecular chaos, i.e. weak convergence of the marginals to the corresponding products of solutions of the respective mean-field equation without cut-off in a quantitative way. Our results thus lead to a deri"},"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":"1307.2999","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2013-07-11T07:30:09Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"e00d1a6cca66798ce9edcd046f3f59428b4006e2102b4ef4d8e185f2b83fea79","abstract_canon_sha256":"88bb9032d7d92077829e31d619941c9610ca3b99bf80a4d18e445e9ef5fda9a9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:58.836277Z","signature_b64":"/vkLE3fCtDMEA658Zr4LRD8Baun7+m+lYXNx8oXa2H/woTMqdBs8okRJdR/EEd0qBrTnRXna2zBHxICDFVLDBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c07700b14a4dde6b084e50045f1775974470e21b5076b28d351eaf02ae994e6","last_reissued_at":"2026-05-18T01:33:58.835831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:58.835831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Mean Field Limits for Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"Niklas Boers, Peter Pickl","submitted_at":"2013-07-11T07:30:09Z","abstract_excerpt":"We present a purely probabilistic proof of propagation of molecular chaos for $N$-particle systems in dimension $3$ with interaction forces scaling like $1/\\vert q\\vert^{\\lambda}$ with $\\lambda<2$ and cut-off at $q = N^{-1/3}$. The proof yields a Gronwall estimate for the maximal distance between exact microscopic and approximate mean-field dynamics. This can be used to show propagation of molecular chaos, i.e. weak convergence of the marginals to the corresponding products of solutions of the respective mean-field equation without cut-off in a quantitative way. Our results thus lead to a deri"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2999","kind":"arxiv","version":2},"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":"1307.2999","created_at":"2026-05-18T01:33:58.835902+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.2999v2","created_at":"2026-05-18T01:33:58.835902+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2999","created_at":"2026-05-18T01:33:58.835902+00:00"},{"alias_kind":"pith_short_12","alias_value":"DQDXACYUUTO6","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"DQDXACYUUTO6NMEE","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"DQDXACYU","created_at":"2026-05-18T12:27:43.054852+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/DQDXACYUUTO6NMEE4UAEL4LXLF","json":"https://pith.science/pith/DQDXACYUUTO6NMEE4UAEL4LXLF.json","graph_json":"https://pith.science/api/pith-number/DQDXACYUUTO6NMEE4UAEL4LXLF/graph.json","events_json":"https://pith.science/api/pith-number/DQDXACYUUTO6NMEE4UAEL4LXLF/events.json","paper":"https://pith.science/paper/DQDXACYU"},"agent_actions":{"view_html":"https://pith.science/pith/DQDXACYUUTO6NMEE4UAEL4LXLF","download_json":"https://pith.science/pith/DQDXACYUUTO6NMEE4UAEL4LXLF.json","view_paper":"https://pith.science/paper/DQDXACYU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.2999&json=true","fetch_graph":"https://pith.science/api/pith-number/DQDXACYUUTO6NMEE4UAEL4LXLF/graph.json","fetch_events":"https://pith.science/api/pith-number/DQDXACYUUTO6NMEE4UAEL4LXLF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DQDXACYUUTO6NMEE4UAEL4LXLF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DQDXACYUUTO6NMEE4UAEL4LXLF/action/storage_attestation","attest_author":"https://pith.science/pith/DQDXACYUUTO6NMEE4UAEL4LXLF/action/author_attestation","sign_citation":"https://pith.science/pith/DQDXACYUUTO6NMEE4UAEL4LXLF/action/citation_signature","submit_replication":"https://pith.science/pith/DQDXACYUUTO6NMEE4UAEL4LXLF/action/replication_record"}},"created_at":"2026-05-18T01:33:58.835902+00:00","updated_at":"2026-05-18T01:33:58.835902+00:00"}