{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:MRKRIC55QXRVKBVMV47EFSK3IQ","short_pith_number":"pith:MRKRIC55","schema_version":"1.0","canonical_sha256":"6455140bbd85e35506acaf3e42c95b44233efbfd887d7d355f5951487114c60e","source":{"kind":"arxiv","id":"1708.07701","version":5},"attestation_state":"computed","paper":{"title":"On the size of chaos in the mean field dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","quant-ph"],"primary_cat":"math.AP","authors_text":"Mario Pulvirenti, Sergio Simonella, Thierry Paul (CMLS)","submitted_at":"2017-08-25T11:53:30Z","abstract_excerpt":"We consider the error arising from the approximation of an N-particle dynamics with its description in terms of a one-particle kinetic equation. We estimate the distance between the j-marginal of the system and the factorized state, obtained in a mean field limit as N $\\rightarrow$ $\\infty$. Our analysis relies on the evolution equation for the \"correlation error\" rather than on the usual BBGKY hierarchy. The rate of convergence is shown to be O(j 2 N) in any bounded interval of time (size of chaos), as expected from heuristic arguments. Our formalism applies to an abstract hierarchical mean f"},"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":"1708.07701","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-25T11:53:30Z","cross_cats_sorted":["math-ph","math.DS","math.MP","quant-ph"],"title_canon_sha256":"514b1c94a15717396fc8c619983ea54148ed2c87ba86e03e618a3ff36479f1fe","abstract_canon_sha256":"dfd2f6ebc91cbefcb4a40df1d4f7c784a7ceb2f93c82b9605e0b933eb6533e80"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:11.195838Z","signature_b64":"PPjg4WzXygbPmtGiEbm4vYqSN9b9eLJtSpoCu5xQtFzdP6nuUJh9n31hnPy8I058lNvptQHr79xAZ/ujct82CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6455140bbd85e35506acaf3e42c95b44233efbfd887d7d355f5951487114c60e","last_reissued_at":"2026-05-18T00:08:11.195390Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:11.195390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the size of chaos in the mean field dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","quant-ph"],"primary_cat":"math.AP","authors_text":"Mario Pulvirenti, Sergio Simonella, Thierry Paul (CMLS)","submitted_at":"2017-08-25T11:53:30Z","abstract_excerpt":"We consider the error arising from the approximation of an N-particle dynamics with its description in terms of a one-particle kinetic equation. We estimate the distance between the j-marginal of the system and the factorized state, obtained in a mean field limit as N $\\rightarrow$ $\\infty$. Our analysis relies on the evolution equation for the \"correlation error\" rather than on the usual BBGKY hierarchy. The rate of convergence is shown to be O(j 2 N) in any bounded interval of time (size of chaos), as expected from heuristic arguments. Our formalism applies to an abstract hierarchical mean f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07701","kind":"arxiv","version":5},"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":"1708.07701","created_at":"2026-05-18T00:08:11.195460+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.07701v5","created_at":"2026-05-18T00:08:11.195460+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07701","created_at":"2026-05-18T00:08:11.195460+00:00"},{"alias_kind":"pith_short_12","alias_value":"MRKRIC55QXRV","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_16","alias_value":"MRKRIC55QXRVKBVM","created_at":"2026-05-18T12:31:31.346846+00:00"},{"alias_kind":"pith_short_8","alias_value":"MRKRIC55","created_at":"2026-05-18T12:31:31.346846+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/MRKRIC55QXRVKBVMV47EFSK3IQ","json":"https://pith.science/pith/MRKRIC55QXRVKBVMV47EFSK3IQ.json","graph_json":"https://pith.science/api/pith-number/MRKRIC55QXRVKBVMV47EFSK3IQ/graph.json","events_json":"https://pith.science/api/pith-number/MRKRIC55QXRVKBVMV47EFSK3IQ/events.json","paper":"https://pith.science/paper/MRKRIC55"},"agent_actions":{"view_html":"https://pith.science/pith/MRKRIC55QXRVKBVMV47EFSK3IQ","download_json":"https://pith.science/pith/MRKRIC55QXRVKBVMV47EFSK3IQ.json","view_paper":"https://pith.science/paper/MRKRIC55","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.07701&json=true","fetch_graph":"https://pith.science/api/pith-number/MRKRIC55QXRVKBVMV47EFSK3IQ/graph.json","fetch_events":"https://pith.science/api/pith-number/MRKRIC55QXRVKBVMV47EFSK3IQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MRKRIC55QXRVKBVMV47EFSK3IQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MRKRIC55QXRVKBVMV47EFSK3IQ/action/storage_attestation","attest_author":"https://pith.science/pith/MRKRIC55QXRVKBVMV47EFSK3IQ/action/author_attestation","sign_citation":"https://pith.science/pith/MRKRIC55QXRVKBVMV47EFSK3IQ/action/citation_signature","submit_replication":"https://pith.science/pith/MRKRIC55QXRVKBVMV47EFSK3IQ/action/replication_record"}},"created_at":"2026-05-18T00:08:11.195460+00:00","updated_at":"2026-05-18T00:08:11.195460+00:00"}