{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:HBS2JPTDVFIMISPPDJVZKQOKBD","short_pith_number":"pith:HBS2JPTD","schema_version":"1.0","canonical_sha256":"3865a4be63a950c449ef1a6b9541ca08d6368837e29da7259a2bb13d96d87111","source":{"kind":"arxiv","id":"1804.04029","version":2},"attestation_state":"computed","paper":{"title":"Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benedict Leimkuhler, Matthias Sachs","submitted_at":"2018-04-11T14:47:58Z","abstract_excerpt":"We discuss the ergodic properties of quasi-Markovian stochastic differential equations, providing general conditions that ensure existence and uniqueness of a smooth invariant distribution and exponential convergence of the evolution operator in suitably weighted $L^{\\infty}$ spaces, which implies the validity of central limit theorem for the respective solution processes. The main new result is an ergodicity condition for the generalized Langevin equation with configuration-dependent noise and (non-)conservative force."},"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":"1804.04029","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-04-11T14:47:58Z","cross_cats_sorted":[],"title_canon_sha256":"3474243c3ce1ba3a0ae7c9e02f19560048fee93c9d201374d5449c29d27a5a43","abstract_canon_sha256":"d29bd1bdf556f2cf9a07783b2e9aa18604e752345b912b4ef004579b8a6baa3c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:09.566124Z","signature_b64":"E2YGtugWka2c67WXPczWjfFsRuD92i/zlrJFE5cmf7KtyWeKlFl/4R8qvpscKKcBW3O8PbqsvfQfG6LAyWMnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3865a4be63a950c449ef1a6b9541ca08d6368837e29da7259a2bb13d96d87111","last_reissued_at":"2026-05-18T00:01:09.565460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:09.565460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Benedict Leimkuhler, Matthias Sachs","submitted_at":"2018-04-11T14:47:58Z","abstract_excerpt":"We discuss the ergodic properties of quasi-Markovian stochastic differential equations, providing general conditions that ensure existence and uniqueness of a smooth invariant distribution and exponential convergence of the evolution operator in suitably weighted $L^{\\infty}$ spaces, which implies the validity of central limit theorem for the respective solution processes. The main new result is an ergodicity condition for the generalized Langevin equation with configuration-dependent noise and (non-)conservative force."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.04029","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":"1804.04029","created_at":"2026-05-18T00:01:09.565569+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.04029v2","created_at":"2026-05-18T00:01:09.565569+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.04029","created_at":"2026-05-18T00:01:09.565569+00:00"},{"alias_kind":"pith_short_12","alias_value":"HBS2JPTDVFIM","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_16","alias_value":"HBS2JPTDVFIMISPP","created_at":"2026-05-18T12:32:28.185984+00:00"},{"alias_kind":"pith_short_8","alias_value":"HBS2JPTD","created_at":"2026-05-18T12:32:28.185984+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/HBS2JPTDVFIMISPPDJVZKQOKBD","json":"https://pith.science/pith/HBS2JPTDVFIMISPPDJVZKQOKBD.json","graph_json":"https://pith.science/api/pith-number/HBS2JPTDVFIMISPPDJVZKQOKBD/graph.json","events_json":"https://pith.science/api/pith-number/HBS2JPTDVFIMISPPDJVZKQOKBD/events.json","paper":"https://pith.science/paper/HBS2JPTD"},"agent_actions":{"view_html":"https://pith.science/pith/HBS2JPTDVFIMISPPDJVZKQOKBD","download_json":"https://pith.science/pith/HBS2JPTDVFIMISPPDJVZKQOKBD.json","view_paper":"https://pith.science/paper/HBS2JPTD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.04029&json=true","fetch_graph":"https://pith.science/api/pith-number/HBS2JPTDVFIMISPPDJVZKQOKBD/graph.json","fetch_events":"https://pith.science/api/pith-number/HBS2JPTDVFIMISPPDJVZKQOKBD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HBS2JPTDVFIMISPPDJVZKQOKBD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HBS2JPTDVFIMISPPDJVZKQOKBD/action/storage_attestation","attest_author":"https://pith.science/pith/HBS2JPTDVFIMISPPDJVZKQOKBD/action/author_attestation","sign_citation":"https://pith.science/pith/HBS2JPTDVFIMISPPDJVZKQOKBD/action/citation_signature","submit_replication":"https://pith.science/pith/HBS2JPTDVFIMISPPDJVZKQOKBD/action/replication_record"}},"created_at":"2026-05-18T00:01:09.565569+00:00","updated_at":"2026-05-18T00:01:09.565569+00:00"}