{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UXWEQXI6LE4T3QG4CCMBNF7CAK","short_pith_number":"pith:UXWEQXI6","schema_version":"1.0","canonical_sha256":"a5ec485d1e59393dc0dc10981697e2029355d080eeda3fbb44fc0cdba893fcdb","source":{"kind":"arxiv","id":"2606.15843","version":2},"attestation_state":"computed","paper":{"title":"Long-time Behaviour of DLRA for SDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Haitao Wang, Jianhai Bao, Yue Wu","submitted_at":"2026-06-14T14:56:43Z","abstract_excerpt":"We study dynamical orthogonal (DO) approximations of stochastic differential equations and investigate their long-time behaviour. The DO formulation represents the solution by a low-rank decomposition and leads to a coupled system consisting of an evolution equation on the Stiefel manifold and a reduced stochastic process. We establish the well-posedness of the strong DO system and derive quantitative error estimates between the original stochastic differential equation and its low-rank approximation in the Wasserstein distance.\n  Our main contribution is the analysis of invariant probability "},"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":"2606.15843","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-14T14:56:43Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"a2eb76e3fa50a3f83fd17b8eff9ff10acbc06126ae6d5b68392bec83bec30e9e","abstract_canon_sha256":"f8e8942b9a492796d940cdfa1c212f00fbc65da57b5b0a77ee871c75066c520d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:12:56.114791Z","signature_b64":"zqz27SaFi6nv3V9EnTCEYKat1wBwP6DFtTLAmgMeJS2lrfvXTeeJTOPrn1XUO05Ygaf94qTYOP84Vzev0x/XBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5ec485d1e59393dc0dc10981697e2029355d080eeda3fbb44fc0cdba893fcdb","last_reissued_at":"2026-06-19T16:12:56.114397Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:12:56.114397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Long-time Behaviour of DLRA for SDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Haitao Wang, Jianhai Bao, Yue Wu","submitted_at":"2026-06-14T14:56:43Z","abstract_excerpt":"We study dynamical orthogonal (DO) approximations of stochastic differential equations and investigate their long-time behaviour. The DO formulation represents the solution by a low-rank decomposition and leads to a coupled system consisting of an evolution equation on the Stiefel manifold and a reduced stochastic process. We establish the well-posedness of the strong DO system and derive quantitative error estimates between the original stochastic differential equation and its low-rank approximation in the Wasserstein distance.\n  Our main contribution is the analysis of invariant probability "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.15843","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.15843/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2606.15843","created_at":"2026-06-19T16:12:56.114463+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.15843v2","created_at":"2026-06-19T16:12:56.114463+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.15843","created_at":"2026-06-19T16:12:56.114463+00:00"},{"alias_kind":"pith_short_12","alias_value":"UXWEQXI6LE4T","created_at":"2026-06-19T16:12:56.114463+00:00"},{"alias_kind":"pith_short_16","alias_value":"UXWEQXI6LE4T3QG4","created_at":"2026-06-19T16:12:56.114463+00:00"},{"alias_kind":"pith_short_8","alias_value":"UXWEQXI6","created_at":"2026-06-19T16:12:56.114463+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/UXWEQXI6LE4T3QG4CCMBNF7CAK","json":"https://pith.science/pith/UXWEQXI6LE4T3QG4CCMBNF7CAK.json","graph_json":"https://pith.science/api/pith-number/UXWEQXI6LE4T3QG4CCMBNF7CAK/graph.json","events_json":"https://pith.science/api/pith-number/UXWEQXI6LE4T3QG4CCMBNF7CAK/events.json","paper":"https://pith.science/paper/UXWEQXI6"},"agent_actions":{"view_html":"https://pith.science/pith/UXWEQXI6LE4T3QG4CCMBNF7CAK","download_json":"https://pith.science/pith/UXWEQXI6LE4T3QG4CCMBNF7CAK.json","view_paper":"https://pith.science/paper/UXWEQXI6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.15843&json=true","fetch_graph":"https://pith.science/api/pith-number/UXWEQXI6LE4T3QG4CCMBNF7CAK/graph.json","fetch_events":"https://pith.science/api/pith-number/UXWEQXI6LE4T3QG4CCMBNF7CAK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UXWEQXI6LE4T3QG4CCMBNF7CAK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UXWEQXI6LE4T3QG4CCMBNF7CAK/action/storage_attestation","attest_author":"https://pith.science/pith/UXWEQXI6LE4T3QG4CCMBNF7CAK/action/author_attestation","sign_citation":"https://pith.science/pith/UXWEQXI6LE4T3QG4CCMBNF7CAK/action/citation_signature","submit_replication":"https://pith.science/pith/UXWEQXI6LE4T3QG4CCMBNF7CAK/action/replication_record"}},"created_at":"2026-06-19T16:12:56.114463+00:00","updated_at":"2026-06-19T16:12:56.114463+00:00"}