{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B4F46Z2XZRXFF2T7DBRRGFHXZ3","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":"dc3d663aa3a56f9c4ed11caa341ebb3c03c9d6600f2fe8f3d001caa30b6133d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-05-09T20:24:05Z","title_canon_sha256":"4095487a8a43d42de6af68271930d85c8510b6953e9e2dfd576b789f943fa6d3"},"schema_version":"1.0","source":{"id":"1705.03526","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03526","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03526v2","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03526","created_at":"2026-05-18T00:12:00Z"},{"alias_kind":"pith_short_12","alias_value":"B4F46Z2XZRXF","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B4F46Z2XZRXFF2T7","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B4F46Z2X","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:b8f5872a5ac6ae8ea5878c65dca8608bbd3a63c56c40656f6271b2d51c6c691c","target":"graph","created_at":"2026-05-18T00:12:00Z","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":"This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of FP equations for the various $n$-time joint distribution functions. Here we present a novel approach to close the hierarchy at the one-time level based on a linearization of the deterministic forces in all members of the hierarchy starting from the second one. This leads to a closed equation for the one-time probability density in the steady state. Consideri","authors_text":"Sabine H. L. Klapp, Sarah A. M. Loos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-05-09T20:24:05Z","title":"Force-linearization closure for non-Markovian Langevin systems with time delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03526","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":"sha256:0a10a1db3b9225bed88e633e4dcdd06769baedae8d2f04c1447e9687a8ea126a","target":"record","created_at":"2026-05-18T00:12:00Z","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":"dc3d663aa3a56f9c4ed11caa341ebb3c03c9d6600f2fe8f3d001caa30b6133d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-05-09T20:24:05Z","title_canon_sha256":"4095487a8a43d42de6af68271930d85c8510b6953e9e2dfd576b789f943fa6d3"},"schema_version":"1.0","source":{"id":"1705.03526","kind":"arxiv","version":2}},"canonical_sha256":"0f0bcf6757cc6e52ea7f18631314f7ced5a268419e20241876347612d46d7801","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f0bcf6757cc6e52ea7f18631314f7ced5a268419e20241876347612d46d7801","first_computed_at":"2026-05-18T00:12:00.476582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:00.476582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p65W/qy7vshKo8W2B8KmPxk7mJqErnG/o9hbJ364fcdFHdcvy3y3afX0zmhsr/AivV+vk+YDHC4SHXcSNdaADw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:00.477258Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03526","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a10a1db3b9225bed88e633e4dcdd06769baedae8d2f04c1447e9687a8ea126a","sha256:b8f5872a5ac6ae8ea5878c65dca8608bbd3a63c56c40656f6271b2d51c6c691c"],"state_sha256":"e6bb8af52adb07c1cb4ddcbd5fc3f267ac126c3617fe6afaf87bb697e2b1ec4e"}