{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AHIZQL3LGKJB7BOJ6FMFMKOKXZ","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":"3fb79a443d155c3ac50f0e5efaeb4162c5287a850fd79823ffda0ff30fcc5266","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-14T19:05:54Z","title_canon_sha256":"ff3f56f186c93e2112da732af6180ae3cdae1388c87cca25edf9d3ad537abe5b"},"schema_version":"1.0","source":{"id":"1212.3567","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.3567","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"arxiv_version","alias_value":"1212.3567v1","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.3567","created_at":"2026-05-18T03:38:24Z"},{"alias_kind":"pith_short_12","alias_value":"AHIZQL3LGKJB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AHIZQL3LGKJB7BOJ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AHIZQL3L","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:5a7629d964ad0604293cab41a862da21abfbaf1aef45c78ef9bfb8e857893c29","target":"graph","created_at":"2026-05-18T03:38:24Z","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":"An existence and uniqueness theorem for a class of stochastic delay differential equations is presented, and the convergence of Euler approximations for these equations is proved under general conditions. Moreover, the rate of almost sure convergence is obtained under local Lipschitz and also under monotonicity conditions.","authors_text":"Istvan Gy\\\"ongy, Sotirios Sabanis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-14T19:05:54Z","title":"A note on Euler approximations for stochastic differential equations with delay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.3567","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":"sha256:1f7fbe85bd4bec5240f4984a91c6ad15a7d2e919b018cf2db282db137f772cef","target":"record","created_at":"2026-05-18T03:38:24Z","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":"3fb79a443d155c3ac50f0e5efaeb4162c5287a850fd79823ffda0ff30fcc5266","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-14T19:05:54Z","title_canon_sha256":"ff3f56f186c93e2112da732af6180ae3cdae1388c87cca25edf9d3ad537abe5b"},"schema_version":"1.0","source":{"id":"1212.3567","kind":"arxiv","version":1}},"canonical_sha256":"01d1982f6b32921f85c9f1585629cabe627dcf05c9d0ee537f54e4c9a9b93964","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"01d1982f6b32921f85c9f1585629cabe627dcf05c9d0ee537f54e4c9a9b93964","first_computed_at":"2026-05-18T03:38:24.273046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:24.273046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sJDcCN5dSFhriWC3iQtzmF0faFpfX3es2nBvR55JSdExFVwSTjGLT2/ZfGeWulsRR1WFpKN9dFVgxaMSksEbBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:24.273615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.3567","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f7fbe85bd4bec5240f4984a91c6ad15a7d2e919b018cf2db282db137f772cef","sha256:5a7629d964ad0604293cab41a862da21abfbaf1aef45c78ef9bfb8e857893c29"],"state_sha256":"6da1d5a249fdab9b7aa5fc5192740cbb10d2adccf80f142b98b62963b7da3ab1"}