{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DMID6GD3I3PQYVPPN2FRI3HWCG","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":"bc990dea0e6af9036c2754b66c23addba8545093a8fe9cf281720a385d781aa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T20:03:13Z","title_canon_sha256":"2dcc6214424b84715167604b0fe553dd72d6795f4c13ee6a109c5cd31dfbf102"},"schema_version":"1.0","source":{"id":"1412.5555","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.5555","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"arxiv_version","alias_value":"1412.5555v2","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.5555","created_at":"2026-05-18T02:27:07Z"},{"alias_kind":"pith_short_12","alias_value":"DMID6GD3I3PQ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DMID6GD3I3PQYVPP","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DMID6GD3","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:8a0990a724ccfb849005ece31ee1cee137b51c3c6ef0dd4a9db59b35b443c5f2","target":"graph","created_at":"2026-05-18T02:27:07Z","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":"The focus of this work is on local stability of a class of nonlinear ordinary differential equations (ODE) that describe limits of empirical measures associated with finite-state weakly interacting N-particle systems. Local Lyapunov functions are identified for several classes of such ODE, including those associated with systems with slow adaptation and Gibbs systems. Using results from [5] and large deviations heuristics, a partial differential equation (PDE) associated with the nonlinear ODE is introduced and it is shown that positive definite subsolutions of this PDE serve as local Lyapunov","authors_text":"Amarjit Budhiraja, Kavita Ramanan, Markus Fischer, Paul Dupuis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T20:03:13Z","title":"Local stability of Kolmogorov forward equations for finite state nonlinear Markov processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5555","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:d0f1fcf34be01cbafea3964acc4f086633b4303b49572282923b25d0fd2f4f72","target":"record","created_at":"2026-05-18T02:27:07Z","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":"bc990dea0e6af9036c2754b66c23addba8545093a8fe9cf281720a385d781aa7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-17T20:03:13Z","title_canon_sha256":"2dcc6214424b84715167604b0fe553dd72d6795f4c13ee6a109c5cd31dfbf102"},"schema_version":"1.0","source":{"id":"1412.5555","kind":"arxiv","version":2}},"canonical_sha256":"1b103f187b46df0c55ef6e8b146cf6118100b76f44487e70471fd18b8275613b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b103f187b46df0c55ef6e8b146cf6118100b76f44487e70471fd18b8275613b","first_computed_at":"2026-05-18T02:27:07.359648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:27:07.359648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1K/nzeLXHk4/FcW36wRR7QvGdVmt3UFNc0jsIEU8p8pJritLbRu0jVSSvXskV05CbkBnhdmT45e4dZmPsQC1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:27:07.360464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.5555","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0f1fcf34be01cbafea3964acc4f086633b4303b49572282923b25d0fd2f4f72","sha256:8a0990a724ccfb849005ece31ee1cee137b51c3c6ef0dd4a9db59b35b443c5f2"],"state_sha256":"236b47c156ca600907fde7898ecaebd21f0e48f471a32a066b309db6afebd605"}