{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UKDRMOBUFVUWUOR55SWUMC5KAD","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":"4b2d8f03c73426b2c7671bd9ec6734641e4dba9c37eac721859b11b702dd5ddc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-13T14:34:28Z","title_canon_sha256":"4e20686c76a0f61086f07f1b3c1cc47587f0f3957b1b50e8666587ec8f3115ed"},"schema_version":"1.0","source":{"id":"1601.03266","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.03266","created_at":"2026-05-18T01:18:38Z"},{"alias_kind":"arxiv_version","alias_value":"1601.03266v2","created_at":"2026-05-18T01:18:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.03266","created_at":"2026-05-18T01:18:38Z"},{"alias_kind":"pith_short_12","alias_value":"UKDRMOBUFVUW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UKDRMOBUFVUWUOR5","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UKDRMOBU","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:51c26819af502ff5b9619adfad42abe3ab58c2942496cdab174ed0579cb46de9","target":"graph","created_at":"2026-05-18T01:18:38Z","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"},"paper":{"abstract_excerpt":"Consider a system of $N$ particles interacting through Newton's second law with Coulomb interaction potential in one spatial dimension or a $\\mathcal{C}^2$ smooth potential in any dimension. We prove that in the mean field limit $N \\to + \\infty$, the $N$ particles system displays instabilities in times of order $\\log N$ for some configurations approximately distributed according to unstable homogeneous equilibria.","authors_text":"Daniel Han-Kwan, Toan T. Nguyen","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-13T14:34:28Z","title":"Instabilities in the mean field limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.03266","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":"sha256:627f308a67bc24b20ebfb26218bf27c6bc57cc401948bb2a3d170fcc56c6ad68","target":"record","created_at":"2026-05-18T01:18:38Z","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":"4b2d8f03c73426b2c7671bd9ec6734641e4dba9c37eac721859b11b702dd5ddc","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-01-13T14:34:28Z","title_canon_sha256":"4e20686c76a0f61086f07f1b3c1cc47587f0f3957b1b50e8666587ec8f3115ed"},"schema_version":"1.0","source":{"id":"1601.03266","kind":"arxiv","version":2}},"canonical_sha256":"a2871638342d696a3a3decad460baa00c0263017bd63ee86bb56fb85abfbbd4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2871638342d696a3a3decad460baa00c0263017bd63ee86bb56fb85abfbbd4a","first_computed_at":"2026-05-18T01:18:38.439018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:38.439018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xuFjgoGhUo8AvDRi3BASR5wk8O8VtDULfdhu6/Wb3K/j+0wZ8kQ65oOPL4q69Y+8bCTuH3b5sawYTpA3RlNBBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:38.439429Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.03266","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:627f308a67bc24b20ebfb26218bf27c6bc57cc401948bb2a3d170fcc56c6ad68","sha256:51c26819af502ff5b9619adfad42abe3ab58c2942496cdab174ed0579cb46de9"],"state_sha256":"91721721d1f04b5fc935256d864cede8914988fd500ce30743a2fca5905f90d5"}