{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:RYFN7CDR4E6OFF63VODF22JNXS","short_pith_number":"pith:RYFN7CDR","schema_version":"1.0","canonical_sha256":"8e0adf8871e13ce297dbab865d692dbc96f32873458f2556da4a8dd21bb1e0a4","source":{"kind":"arxiv","id":"1404.2330","version":4},"attestation_state":"computed","paper":{"title":"The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Austin McDaniel, Giovanni Volpe, Jan Wehr, Scott Hottovy","submitted_at":"2014-04-08T23:18:22Z","abstract_excerpt":"We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our systems have arbitrary state-dependent friction and noise coefficients. We identify the limiting equation and, in particular, the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation. The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter. The result is sufficiently general to include systems driv"},"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":"1404.2330","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-04-08T23:18:22Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"7eba27c10af8859dab7bf7cb119b610fd4a8efbb44e6d1ae069c78230e08c3a8","abstract_canon_sha256":"abed629992441eac372937aae8ca190f4633b4c9400d7c90bad580434ef02af6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:07.517981Z","signature_b64":"cjn+z4UIm9D3x70/yDMhlosrvujAzlvQX4pFgyfQ/vEvIfqPCoRVF5VSnuDjYL6il4bJQUICCzFoKm6qs7LpDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e0adf8871e13ce297dbab865d692dbc96f32873458f2556da4a8dd21bb1e0a4","last_reissued_at":"2026-05-18T01:16:07.517237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:07.517237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Smoluchowski-Kramers limit of stochastic differential equations with arbitrary state-dependent friction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Austin McDaniel, Giovanni Volpe, Jan Wehr, Scott Hottovy","submitted_at":"2014-04-08T23:18:22Z","abstract_excerpt":"We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our systems have arbitrary state-dependent friction and noise coefficients. We identify the limiting equation and, in particular, the additional drift term that appears in the limit is expressed in terms of the solution to a Lyapunov matrix equation. The proof uses a theory of convergence of stochastic integrals developed by Kurtz and Protter. The result is sufficiently general to include systems driv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2330","kind":"arxiv","version":4},"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":"1404.2330","created_at":"2026-05-18T01:16:07.517347+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.2330v4","created_at":"2026-05-18T01:16:07.517347+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2330","created_at":"2026-05-18T01:16:07.517347+00:00"},{"alias_kind":"pith_short_12","alias_value":"RYFN7CDR4E6O","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"RYFN7CDR4E6OFF63","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"RYFN7CDR","created_at":"2026-05-18T12:28:46.137349+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/RYFN7CDR4E6OFF63VODF22JNXS","json":"https://pith.science/pith/RYFN7CDR4E6OFF63VODF22JNXS.json","graph_json":"https://pith.science/api/pith-number/RYFN7CDR4E6OFF63VODF22JNXS/graph.json","events_json":"https://pith.science/api/pith-number/RYFN7CDR4E6OFF63VODF22JNXS/events.json","paper":"https://pith.science/paper/RYFN7CDR"},"agent_actions":{"view_html":"https://pith.science/pith/RYFN7CDR4E6OFF63VODF22JNXS","download_json":"https://pith.science/pith/RYFN7CDR4E6OFF63VODF22JNXS.json","view_paper":"https://pith.science/paper/RYFN7CDR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.2330&json=true","fetch_graph":"https://pith.science/api/pith-number/RYFN7CDR4E6OFF63VODF22JNXS/graph.json","fetch_events":"https://pith.science/api/pith-number/RYFN7CDR4E6OFF63VODF22JNXS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RYFN7CDR4E6OFF63VODF22JNXS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RYFN7CDR4E6OFF63VODF22JNXS/action/storage_attestation","attest_author":"https://pith.science/pith/RYFN7CDR4E6OFF63VODF22JNXS/action/author_attestation","sign_citation":"https://pith.science/pith/RYFN7CDR4E6OFF63VODF22JNXS/action/citation_signature","submit_replication":"https://pith.science/pith/RYFN7CDR4E6OFF63VODF22JNXS/action/replication_record"}},"created_at":"2026-05-18T01:16:07.517347+00:00","updated_at":"2026-05-18T01:16:07.517347+00:00"}