{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:GWXUJI7EV7WXD5POSZM6B7SSAR","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":"f067eccb68156e645ae69e5e9f339962005202dd0c7b87cb46f206522fb3d8e8","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-19T09:11:44Z","title_canon_sha256":"ceaaac58fea6f2c6d892bbd892d935002b46a6e541f02f790dd9a34b34de9776"},"schema_version":"1.0","source":{"id":"2505.12883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.12883","created_at":"2026-07-05T11:05:11Z"},{"alias_kind":"arxiv_version","alias_value":"2505.12883v1","created_at":"2026-07-05T11:05:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.12883","created_at":"2026-07-05T11:05:11Z"},{"alias_kind":"pith_short_12","alias_value":"GWXUJI7EV7WX","created_at":"2026-07-05T11:05:11Z"},{"alias_kind":"pith_short_16","alias_value":"GWXUJI7EV7WXD5PO","created_at":"2026-07-05T11:05:11Z"},{"alias_kind":"pith_short_8","alias_value":"GWXUJI7E","created_at":"2026-07-05T11:05:11Z"}],"graph_snapshots":[{"event_id":"sha256:2b2556351b04c9895c29cc2eec0e5c1b09b65a6a6d2f7e978bea63a67dc76e4f","target":"graph","created_at":"2026-07-05T11:05:11Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.12883/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the approximation of stochastic delay differential equations (SDDEs) via the backward Euler-Maruyama (BEM) method under generalized monotonicity and Khasminskii-type conditions in the infinite horizon. First, by establishing the uniform moment boundedness and finite-time strong convergence of the BEM method, we prove that for sufficiently small step sizes, the numerical approximations strongly converge to the underlying solution in the infinite horizon with a rate of $1/2$, which coincides with the optimal finite-time strong convergence rate.\n  Next, we establish the un","authors_text":"Hongjiong Tian, Yudong Wang","cross_cats":["cs.NA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-19T09:11:44Z","title":"Implicit numerical approximation for stochastic delay differential equations with the nonlinear diffusion term in the infinite horizon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.12883","kind":"arxiv","version":1},"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:cd30410eb7439f415899c4fb891a978d9960bdd34f3de649cabda9cd5e03ece0","target":"record","created_at":"2026-07-05T11:05:11Z","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":"f067eccb68156e645ae69e5e9f339962005202dd0c7b87cb46f206522fb3d8e8","cross_cats_sorted":["cs.NA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2025-05-19T09:11:44Z","title_canon_sha256":"ceaaac58fea6f2c6d892bbd892d935002b46a6e541f02f790dd9a34b34de9776"},"schema_version":"1.0","source":{"id":"2505.12883","kind":"arxiv","version":1}},"canonical_sha256":"35af44a3e4afed71f5ee9659e0fe52044a17595b0ddcfe25467590297dee15bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35af44a3e4afed71f5ee9659e0fe52044a17595b0ddcfe25467590297dee15bb","first_computed_at":"2026-07-05T11:05:11.177632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:05:11.177632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UC71AOt17qIVOf6wlwzOd++tvuvFeO7vXnnvFouDnpTuwXL794kYBtChac4/3Py29S298WwM8D8lF5G01GXZDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:05:11.178049Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.12883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd30410eb7439f415899c4fb891a978d9960bdd34f3de649cabda9cd5e03ece0","sha256:2b2556351b04c9895c29cc2eec0e5c1b09b65a6a6d2f7e978bea63a67dc76e4f"],"state_sha256":"5eb34d5f838a161ca24bf17446ab0496ee805f290c3c2ee78ece149cceb42da5"}