{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:2EBNO7DM5KFHXJAXKVQJ4IBRTI","short_pith_number":"pith:2EBNO7DM","canonical_record":{"source":{"id":"1407.5149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-19T05:57:24Z","cross_cats_sorted":[],"title_canon_sha256":"1c8af1f138892db3038d600c5c1be5d39d0ccc73653f542e66d9b57f82c69ec0","abstract_canon_sha256":"d6dce791e22adc5ede7ebf0be4efc376f945e7648621f482e4a0fec84d8454b5"},"schema_version":"1.0"},"canonical_sha256":"d102d77c6cea8a7ba41755609e20319a3488d012f93edbe28471371e09df96ad","source":{"kind":"arxiv","id":"1407.5149","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5149","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5149v1","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5149","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"pith_short_12","alias_value":"2EBNO7DM5KFH","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2EBNO7DM5KFHXJAX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2EBNO7DM","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:2EBNO7DM5KFHXJAXKVQJ4IBRTI","target":"record","payload":{"canonical_record":{"source":{"id":"1407.5149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-19T05:57:24Z","cross_cats_sorted":[],"title_canon_sha256":"1c8af1f138892db3038d600c5c1be5d39d0ccc73653f542e66d9b57f82c69ec0","abstract_canon_sha256":"d6dce791e22adc5ede7ebf0be4efc376f945e7648621f482e4a0fec84d8454b5"},"schema_version":"1.0"},"canonical_sha256":"d102d77c6cea8a7ba41755609e20319a3488d012f93edbe28471371e09df96ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:14.839688Z","signature_b64":"H0F5CPSf+9Q/aGtZgfm0/HGLLOPSsUM1+AZ4l+NFMYc+cqXpNjP5csZla0ET0HrcNDoGREFfvorVle3GeXysAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d102d77c6cea8a7ba41755609e20319a3488d012f93edbe28471371e09df96ad","last_reissued_at":"2026-05-18T02:47:14.839061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:14.839061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.5149","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KvEblmfr0T7JEfh0i56BpsxTR2r5A0kSaPYCQilp773XDlH6x2RusWEa88BVj+YSkFYAyjSWT3ZkrbLoKmHFBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:27:33.317253Z"},"content_sha256":"1ec874bef7f904c28d2a0bf2e40aa5484f41b5a2366585857d5e67695ccf49c0","schema_version":"1.0","event_id":"sha256:1ec874bef7f904c28d2a0bf2e40aa5484f41b5a2366585857d5e67695ccf49c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:2EBNO7DM5KFHXJAXKVQJ4IBRTI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of solutions of mixed stochastic delay differential equations with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Georgiy Shevchenko, Taras Shalaiko, Yuliya Mishura","submitted_at":"2014-07-19T05:57:24Z","abstract_excerpt":"The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a $\\gamma$-H\\\"older continuous process with $\\gamma>1/2$ (e.g. a fractional Brownian motion with Hurst parameter greater than $1/2$). It is shown that its solution depends continuously on the coefficients and the initial data. Two applications of this result are given: the convergence of solutions to equations with vanishing delay to the solution of equation without delay and the convergence of Euler approximations for mixed stochastic differential equations. As a side result of indep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5149","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:47:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WPKo1x+IM33hVKcD0URYxrYt0B/21vfRtl2GfQmz96m98nXwybcO1aGrpPStn5LyWi7GAlGjuusjynj7cumkDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:27:33.317617Z"},"content_sha256":"6ab7f8a2ffcf881ea6e8245a77d66d56d5c826f477d4a0dcfa1d775c1d49a573","schema_version":"1.0","event_id":"sha256:6ab7f8a2ffcf881ea6e8245a77d66d56d5c826f477d4a0dcfa1d775c1d49a573"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2EBNO7DM5KFHXJAXKVQJ4IBRTI/bundle.json","state_url":"https://pith.science/pith/2EBNO7DM5KFHXJAXKVQJ4IBRTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2EBNO7DM5KFHXJAXKVQJ4IBRTI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T15:27:33Z","links":{"resolver":"https://pith.science/pith/2EBNO7DM5KFHXJAXKVQJ4IBRTI","bundle":"https://pith.science/pith/2EBNO7DM5KFHXJAXKVQJ4IBRTI/bundle.json","state":"https://pith.science/pith/2EBNO7DM5KFHXJAXKVQJ4IBRTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2EBNO7DM5KFHXJAXKVQJ4IBRTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:2EBNO7DM5KFHXJAXKVQJ4IBRTI","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":"d6dce791e22adc5ede7ebf0be4efc376f945e7648621f482e4a0fec84d8454b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-19T05:57:24Z","title_canon_sha256":"1c8af1f138892db3038d600c5c1be5d39d0ccc73653f542e66d9b57f82c69ec0"},"schema_version":"1.0","source":{"id":"1407.5149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.5149","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"arxiv_version","alias_value":"1407.5149v1","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.5149","created_at":"2026-05-18T02:47:14Z"},{"alias_kind":"pith_short_12","alias_value":"2EBNO7DM5KFH","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"2EBNO7DM5KFHXJAX","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"2EBNO7DM","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:6ab7f8a2ffcf881ea6e8245a77d66d56d5c826f477d4a0dcfa1d775c1d49a573","target":"graph","created_at":"2026-05-18T02:47:14Z","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":"The paper is concerned with a mixed stochastic delay differential equation involving both a Wiener process and a $\\gamma$-H\\\"older continuous process with $\\gamma>1/2$ (e.g. a fractional Brownian motion with Hurst parameter greater than $1/2$). It is shown that its solution depends continuously on the coefficients and the initial data. Two applications of this result are given: the convergence of solutions to equations with vanishing delay to the solution of equation without delay and the convergence of Euler approximations for mixed stochastic differential equations. As a side result of indep","authors_text":"Georgiy Shevchenko, Taras Shalaiko, Yuliya Mishura","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-19T05:57:24Z","title":"Convergence of solutions of mixed stochastic delay differential equations with applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5149","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":"sha256:1ec874bef7f904c28d2a0bf2e40aa5484f41b5a2366585857d5e67695ccf49c0","target":"record","created_at":"2026-05-18T02:47:14Z","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":"d6dce791e22adc5ede7ebf0be4efc376f945e7648621f482e4a0fec84d8454b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-19T05:57:24Z","title_canon_sha256":"1c8af1f138892db3038d600c5c1be5d39d0ccc73653f542e66d9b57f82c69ec0"},"schema_version":"1.0","source":{"id":"1407.5149","kind":"arxiv","version":1}},"canonical_sha256":"d102d77c6cea8a7ba41755609e20319a3488d012f93edbe28471371e09df96ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d102d77c6cea8a7ba41755609e20319a3488d012f93edbe28471371e09df96ad","first_computed_at":"2026-05-18T02:47:14.839061Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:14.839061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H0F5CPSf+9Q/aGtZgfm0/HGLLOPSsUM1+AZ4l+NFMYc+cqXpNjP5csZla0ET0HrcNDoGREFfvorVle3GeXysAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:14.839688Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.5149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1ec874bef7f904c28d2a0bf2e40aa5484f41b5a2366585857d5e67695ccf49c0","sha256:6ab7f8a2ffcf881ea6e8245a77d66d56d5c826f477d4a0dcfa1d775c1d49a573"],"state_sha256":"dae5ad91d5d509c7ea6d9748baa8c5338dc0b723c2ebc268894f8edbc89833c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iw8JOe6IQp+iikQRLdPDSbytBUFtIRr8umuCGgZAQtQ/q3s2ZQg8MK4wgsxrrlu2Efnm2tUJ3ztPJMNqgosFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:27:33.319823Z","bundle_sha256":"3335c2ce86e079b7d41be335c2e59cc8148bc6a6c10d1d153bf0fd0d6e3ea1bc"}}