{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AVZPFCB3RT6OMF3CM3YXZBWJBF","short_pith_number":"pith:AVZPFCB3","canonical_record":{"source":{"id":"1310.6169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-23T10:06:54Z","cross_cats_sorted":[],"title_canon_sha256":"9a5bc624f6ef0ed7163389c2fa2d12a69e5d379d05c1e8af0b446b724413ac7b","abstract_canon_sha256":"b1a2fd69c00b9914a2f227b43a8341de39c6f600d2275564827c65cff9d5c123"},"schema_version":"1.0"},"canonical_sha256":"0572f2883b8cfce6176266f17c86c9094c67462f19742b04052e2779a962e128","source":{"kind":"arxiv","id":"1310.6169","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6169","created_at":"2026-05-18T03:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6169v1","created_at":"2026-05-18T03:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6169","created_at":"2026-05-18T03:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"AVZPFCB3RT6O","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AVZPFCB3RT6OMF3C","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AVZPFCB3","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AVZPFCB3RT6OMF3CM3YXZBWJBF","target":"record","payload":{"canonical_record":{"source":{"id":"1310.6169","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-23T10:06:54Z","cross_cats_sorted":[],"title_canon_sha256":"9a5bc624f6ef0ed7163389c2fa2d12a69e5d379d05c1e8af0b446b724413ac7b","abstract_canon_sha256":"b1a2fd69c00b9914a2f227b43a8341de39c6f600d2275564827c65cff9d5c123"},"schema_version":"1.0"},"canonical_sha256":"0572f2883b8cfce6176266f17c86c9094c67462f19742b04052e2779a962e128","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:21.211407Z","signature_b64":"gDfbOLXl1cesW14gEjExDnahThcP+sg6TiCPYAtN6iqv4m5yyobsH7B5gEF8yYWmu8t4TD2Z6I0JCvZ19yPTDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0572f2883b8cfce6176266f17c86c9094c67462f19742b04052e2779a962e128","last_reissued_at":"2026-05-18T03:09:21.210559Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:21.210559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.6169","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":"2026-05-18T03:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XyGSnTwHaQ/Gxd6CPRuwBIix+tdVCnNQr1pgn4pxfwiMUUjNkYQzGqmgbnMAWdXn7N/bCnpcqBy3Mvrpl8vTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:36:38.142249Z"},"content_sha256":"b48721c849bc9ee94924c1f45f7ed5c26bffe85dd72c813befeae9b58efd55ee","schema_version":"1.0","event_id":"sha256:b48721c849bc9ee94924c1f45f7ed5c26bffe85dd72c813befeae9b58efd55ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AVZPFCB3RT6OMF3CM3YXZBWJBF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Taylor expansions for the expectation of functionals of diffusion processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andreas R\\\"o{\\ss}ler","submitted_at":"2013-10-23T10:06:54Z","abstract_excerpt":"Stochastic Taylor expansions of the expectation of functionals applied to diffusion processes which are solutions of stochastic differential equation systems are introduced. Taylor formulas w.r.t. increments of the time are presented for both, It\\^o and Stratonovich stochastic differential equation systems with multi-dimensional Wiener processes. Due to the very complex formulas arising for higher order expansions, an advantageous graphical representation by coloured trees is developed. The convergence of truncated formulas is analyzed and estimates for the truncation error are calculated. Fin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6169","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":"2026-05-18T03:09:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ZK8EjBReuL2GJaotWgS3KTCOT/wZkTPmzFZOC06z+AbNCchtcCLdeb9nP+6i/4kpMkSwIiWNyZkWbP3tbBDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:36:38.142609Z"},"content_sha256":"cd0dbc3835d3e6eade7decc7cb20bc0e4eb1274990a7e153f83c3ab181beb48a","schema_version":"1.0","event_id":"sha256:cd0dbc3835d3e6eade7decc7cb20bc0e4eb1274990a7e153f83c3ab181beb48a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AVZPFCB3RT6OMF3CM3YXZBWJBF/bundle.json","state_url":"https://pith.science/pith/AVZPFCB3RT6OMF3CM3YXZBWJBF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AVZPFCB3RT6OMF3CM3YXZBWJBF/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":"2026-06-24T05:36:38Z","links":{"resolver":"https://pith.science/pith/AVZPFCB3RT6OMF3CM3YXZBWJBF","bundle":"https://pith.science/pith/AVZPFCB3RT6OMF3CM3YXZBWJBF/bundle.json","state":"https://pith.science/pith/AVZPFCB3RT6OMF3CM3YXZBWJBF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AVZPFCB3RT6OMF3CM3YXZBWJBF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AVZPFCB3RT6OMF3CM3YXZBWJBF","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":"b1a2fd69c00b9914a2f227b43a8341de39c6f600d2275564827c65cff9d5c123","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-23T10:06:54Z","title_canon_sha256":"9a5bc624f6ef0ed7163389c2fa2d12a69e5d379d05c1e8af0b446b724413ac7b"},"schema_version":"1.0","source":{"id":"1310.6169","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.6169","created_at":"2026-05-18T03:09:21Z"},{"alias_kind":"arxiv_version","alias_value":"1310.6169v1","created_at":"2026-05-18T03:09:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6169","created_at":"2026-05-18T03:09:21Z"},{"alias_kind":"pith_short_12","alias_value":"AVZPFCB3RT6O","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AVZPFCB3RT6OMF3C","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AVZPFCB3","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:cd0dbc3835d3e6eade7decc7cb20bc0e4eb1274990a7e153f83c3ab181beb48a","target":"graph","created_at":"2026-05-18T03:09:21Z","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":"Stochastic Taylor expansions of the expectation of functionals applied to diffusion processes which are solutions of stochastic differential equation systems are introduced. Taylor formulas w.r.t. increments of the time are presented for both, It\\^o and Stratonovich stochastic differential equation systems with multi-dimensional Wiener processes. Due to the very complex formulas arising for higher order expansions, an advantageous graphical representation by coloured trees is developed. The convergence of truncated formulas is analyzed and estimates for the truncation error are calculated. Fin","authors_text":"Andreas R\\\"o{\\ss}ler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-23T10:06:54Z","title":"Stochastic Taylor expansions for the expectation of functionals of diffusion processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6169","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:b48721c849bc9ee94924c1f45f7ed5c26bffe85dd72c813befeae9b58efd55ee","target":"record","created_at":"2026-05-18T03:09:21Z","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":"b1a2fd69c00b9914a2f227b43a8341de39c6f600d2275564827c65cff9d5c123","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-23T10:06:54Z","title_canon_sha256":"9a5bc624f6ef0ed7163389c2fa2d12a69e5d379d05c1e8af0b446b724413ac7b"},"schema_version":"1.0","source":{"id":"1310.6169","kind":"arxiv","version":1}},"canonical_sha256":"0572f2883b8cfce6176266f17c86c9094c67462f19742b04052e2779a962e128","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0572f2883b8cfce6176266f17c86c9094c67462f19742b04052e2779a962e128","first_computed_at":"2026-05-18T03:09:21.210559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:21.210559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gDfbOLXl1cesW14gEjExDnahThcP+sg6TiCPYAtN6iqv4m5yyobsH7B5gEF8yYWmu8t4TD2Z6I0JCvZ19yPTDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:21.211407Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.6169","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b48721c849bc9ee94924c1f45f7ed5c26bffe85dd72c813befeae9b58efd55ee","sha256:cd0dbc3835d3e6eade7decc7cb20bc0e4eb1274990a7e153f83c3ab181beb48a"],"state_sha256":"95ee3c11ea5d5b3b4cf94e6341ea7fd927363eb30770df9560a4acf821ef5b6a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gOVRA7psLkltjmsMBcMTojW64gMNxn1eQDpA0cL/JuorHmmNwM4jZ+6lhusTys0GYoFViMjvw1lSYSgIpt9tCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:36:38.144526Z","bundle_sha256":"741a5442dad42d8a25a24f17c65818ac99099f4b5541fc8f9350a05c2e9cb6ec"}}