{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:P5VY5CT6EOLDFG4BKV4L2Q6X6R","short_pith_number":"pith:P5VY5CT6","canonical_record":{"source":{"id":"1009.4728","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-23T21:26:42Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"4935ed41a8deaeedce1072fe3f7fd32aabc857e1f96c529f3e9d2aecf8639742","abstract_canon_sha256":"bf8eb6e719f54725030c39eb45e245ab25a136505291b2339db56e1b797772e2"},"schema_version":"1.0"},"canonical_sha256":"7f6b8e8a7e2396329b815578bd43d7f45a8fd8628c45de502e079ea826101d43","source":{"kind":"arxiv","id":"1009.4728","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4728","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4728v3","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4728","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"pith_short_12","alias_value":"P5VY5CT6EOLD","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P5VY5CT6EOLDFG4B","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P5VY5CT6","created_at":"2026-05-18T12:26:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:P5VY5CT6EOLDFG4BKV4L2Q6X6R","target":"record","payload":{"canonical_record":{"source":{"id":"1009.4728","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-23T21:26:42Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"4935ed41a8deaeedce1072fe3f7fd32aabc857e1f96c529f3e9d2aecf8639742","abstract_canon_sha256":"bf8eb6e719f54725030c39eb45e245ab25a136505291b2339db56e1b797772e2"},"schema_version":"1.0"},"canonical_sha256":"7f6b8e8a7e2396329b815578bd43d7f45a8fd8628c45de502e079ea826101d43","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:35:04.547591Z","signature_b64":"YTsiJjNN+D2RBPV8OSiNaqn7UDcpoI6Lr35qnBnSc4jYJEG4hoHrjEII1jYyFb1oaTRsAYbog6N6uXe2AzrMCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f6b8e8a7e2396329b815578bd43d7f45a8fd8628c45de502e079ea826101d43","last_reissued_at":"2026-05-18T04:35:04.547173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:35:04.547173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.4728","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:35:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QYRtH3usBqxNdp5cwgl4eDayAxOf3WvcL3MP8vMksbp8Y4N94wZ/igRz3k8ZSahEqvdLH0Mqm59T6FKnvhukBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T04:26:18.143777Z"},"content_sha256":"879bbc90f7b092c8b9c3aeb7dd3b21f973d110b3e7e6d7d491da696edeca12a5","schema_version":"1.0","event_id":"sha256:879bbc90f7b092c8b9c3aeb7dd3b21f973d110b3e7e6d7d491da696edeca12a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:P5VY5CT6EOLDFG4BKV4L2Q6X6R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the rate of convergence of weak Euler approximation for non-degenerate SDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"C. Zhang, R. Mikulevicius","submitted_at":"2010-09-23T21:26:42Z","abstract_excerpt":"The paper estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures. The equation considered has a non-degenerate main part whose jump intensity measure is absolutely continuous with respect to the Levy measure of a spherically-symmetric stable process. It includes the nondegenerate diffusions and SDEs driven by Levy processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4728","kind":"arxiv","version":3},"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":"2026-05-18T04:35:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"38SHTRZp3pcOvaoJalwCCd5UXz2+iizxrzxa5BAAMXwVZaEedeFLqJBR4HIXUVcEDDhtY0pbNVnBrGjYAs1SDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T04:26:18.144122Z"},"content_sha256":"54cbaf9d16831f7c24575382b3a303a59082da5a906132fa63b1c64595175c33","schema_version":"1.0","event_id":"sha256:54cbaf9d16831f7c24575382b3a303a59082da5a906132fa63b1c64595175c33"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P5VY5CT6EOLDFG4BKV4L2Q6X6R/bundle.json","state_url":"https://pith.science/pith/P5VY5CT6EOLDFG4BKV4L2Q6X6R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P5VY5CT6EOLDFG4BKV4L2Q6X6R/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":"2026-07-04T04:26:18Z","links":{"resolver":"https://pith.science/pith/P5VY5CT6EOLDFG4BKV4L2Q6X6R","bundle":"https://pith.science/pith/P5VY5CT6EOLDFG4BKV4L2Q6X6R/bundle.json","state":"https://pith.science/pith/P5VY5CT6EOLDFG4BKV4L2Q6X6R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P5VY5CT6EOLDFG4BKV4L2Q6X6R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:P5VY5CT6EOLDFG4BKV4L2Q6X6R","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":"bf8eb6e719f54725030c39eb45e245ab25a136505291b2339db56e1b797772e2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-23T21:26:42Z","title_canon_sha256":"4935ed41a8deaeedce1072fe3f7fd32aabc857e1f96c529f3e9d2aecf8639742"},"schema_version":"1.0","source":{"id":"1009.4728","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.4728","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"arxiv_version","alias_value":"1009.4728v3","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4728","created_at":"2026-05-18T04:35:04Z"},{"alias_kind":"pith_short_12","alias_value":"P5VY5CT6EOLD","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"P5VY5CT6EOLDFG4B","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"P5VY5CT6","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:54cbaf9d16831f7c24575382b3a303a59082da5a906132fa63b1c64595175c33","target":"graph","created_at":"2026-05-18T04:35:04Z","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 estimates the rate of convergence of the weak Euler approximation for the solutions of SDEs with Hoelder continuous coefficients driven by point and martingale measures. The equation considered has a non-degenerate main part whose jump intensity measure is absolutely continuous with respect to the Levy measure of a spherically-symmetric stable process. It includes the nondegenerate diffusions and SDEs driven by Levy processes.","authors_text":"C. Zhang, R. Mikulevicius","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-23T21:26:42Z","title":"On the rate of convergence of weak Euler approximation for non-degenerate SDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4728","kind":"arxiv","version":3},"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":"sha256:879bbc90f7b092c8b9c3aeb7dd3b21f973d110b3e7e6d7d491da696edeca12a5","target":"record","created_at":"2026-05-18T04:35:04Z","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":"bf8eb6e719f54725030c39eb45e245ab25a136505291b2339db56e1b797772e2","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-23T21:26:42Z","title_canon_sha256":"4935ed41a8deaeedce1072fe3f7fd32aabc857e1f96c529f3e9d2aecf8639742"},"schema_version":"1.0","source":{"id":"1009.4728","kind":"arxiv","version":3}},"canonical_sha256":"7f6b8e8a7e2396329b815578bd43d7f45a8fd8628c45de502e079ea826101d43","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f6b8e8a7e2396329b815578bd43d7f45a8fd8628c45de502e079ea826101d43","first_computed_at":"2026-05-18T04:35:04.547173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:35:04.547173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YTsiJjNN+D2RBPV8OSiNaqn7UDcpoI6Lr35qnBnSc4jYJEG4hoHrjEII1jYyFb1oaTRsAYbog6N6uXe2AzrMCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:35:04.547591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.4728","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:879bbc90f7b092c8b9c3aeb7dd3b21f973d110b3e7e6d7d491da696edeca12a5","sha256:54cbaf9d16831f7c24575382b3a303a59082da5a906132fa63b1c64595175c33"],"state_sha256":"c85897ca92a31b73f99cdc803cd0cef3d0da86e64fe49823a4771f4b3ee0d738"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Bz7Hja9cydjN3SypsfbVHznXWjSgJ/IpI6p0yAvZUtJPQXa7zuKWxhwdgyhkHG4QKQELwVklhsQXFz51nz3BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T04:26:18.146099Z","bundle_sha256":"c18fc118d729f859673efc80b8689e65525835b2b5258a4ecfb445960a8c2ba9"}}