{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LLERE35UBFGBZDT54WJRC5AEAY","short_pith_number":"pith:LLERE35U","canonical_record":{"source":{"id":"1603.08756","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:08:05Z","cross_cats_sorted":[],"title_canon_sha256":"dfce4e33b41e654bc341b6668eedadb49b34ed2cafc0bb79d8ce937a830c14e1","abstract_canon_sha256":"0c05f87e630e02cfc48b86d4c3bb20425df1dfaf1994e0a6cf28dfd72d2ca5d7"},"schema_version":"1.0"},"canonical_sha256":"5ac9126fb4094c1c8e7de593117404060db9b0efb8c4271efa43b36573730b19","source":{"kind":"arxiv","id":"1603.08756","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08756","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08756v2","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08756","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"pith_short_12","alias_value":"LLERE35UBFGB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LLERE35UBFGBZDT5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LLERE35U","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LLERE35UBFGBZDT54WJRC5AEAY","target":"record","payload":{"canonical_record":{"source":{"id":"1603.08756","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:08:05Z","cross_cats_sorted":[],"title_canon_sha256":"dfce4e33b41e654bc341b6668eedadb49b34ed2cafc0bb79d8ce937a830c14e1","abstract_canon_sha256":"0c05f87e630e02cfc48b86d4c3bb20425df1dfaf1994e0a6cf28dfd72d2ca5d7"},"schema_version":"1.0"},"canonical_sha256":"5ac9126fb4094c1c8e7de593117404060db9b0efb8c4271efa43b36573730b19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:29.691690Z","signature_b64":"zP/xpC3bi9P68tra4rQCj4btHK2jivKq3dLNB5Ds3ROKYREdZlpxwqpyEd+EybZsPjhdVqhn/jXFAWDotamTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ac9126fb4094c1c8e7de593117404060db9b0efb8c4271efa43b36573730b19","last_reissued_at":"2026-05-18T01:12:29.691335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:29.691335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.08756","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Je3LEAkFYbIO6CveusBjY+Gc3mmaA9nmgH11SWb2IQF/8GCAIv28+nX+bM8Zb4fuRocObBlpqIUcPb+OlsY2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:57:45.148392Z"},"content_sha256":"2a7cff83332a56cc1880135ba05e5e989f11b9fa3855a68cb54d43fbe405d3ba","schema_version":"1.0","event_id":"sha256:2a7cff83332a56cc1880135ba05e5e989f11b9fa3855a68cb54d43fbe405d3ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LLERE35UBFGBZDT54WJRC5AEAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak error analysis via functional It\\^o calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Felix Lindner, Mih\\'aly Kov\\'acs","submitted_at":"2016-03-29T13:08:05Z","abstract_excerpt":"We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\\^o calculus, such as the functional It\\^o formula and functional Kolmogorov equation, we derive a general representation formula for the weak error $E(f(X_T)-f(\\tilde X_T))$, where $X_T$ and $\\tilde X_T$ are the paths of the solution process and its approximation up to time T. The functional $f:C([0,T],R^d)\\to R$ is assumed to be twice continuously Fr\\'echet differentiable w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08756","kind":"arxiv","version":2},"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":"2026-05-18T01:12:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RO2hRRa497Ts4y82gQ22RZN72wVSsL6Oz5ss1w/uZYnpCRn1G/UY2iczcslVWrHEyZFLFT+8pAC6QTgcuwoPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T03:57:45.148748Z"},"content_sha256":"331be73e97377356cce3d9d269f4db80e3ecbd7002b5301b4aa52f61c9acdd28","schema_version":"1.0","event_id":"sha256:331be73e97377356cce3d9d269f4db80e3ecbd7002b5301b4aa52f61c9acdd28"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY/bundle.json","state_url":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LLERE35UBFGBZDT54WJRC5AEAY/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":"2026-05-30T03:57:45Z","links":{"resolver":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY","bundle":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY/bundle.json","state":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LLERE35UBFGBZDT54WJRC5AEAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LLERE35UBFGBZDT54WJRC5AEAY","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":"0c05f87e630e02cfc48b86d4c3bb20425df1dfaf1994e0a6cf28dfd72d2ca5d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:08:05Z","title_canon_sha256":"dfce4e33b41e654bc341b6668eedadb49b34ed2cafc0bb79d8ce937a830c14e1"},"schema_version":"1.0","source":{"id":"1603.08756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08756","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08756v2","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08756","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"pith_short_12","alias_value":"LLERE35UBFGB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LLERE35UBFGBZDT5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LLERE35U","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:331be73e97377356cce3d9d269f4db80e3ecbd7002b5301b4aa52f61c9acdd28","target":"graph","created_at":"2026-05-18T01:12:29Z","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":"We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\\^o calculus, such as the functional It\\^o formula and functional Kolmogorov equation, we derive a general representation formula for the weak error $E(f(X_T)-f(\\tilde X_T))$, where $X_T$ and $\\tilde X_T$ are the paths of the solution process and its approximation up to time T. The functional $f:C([0,T],R^d)\\to R$ is assumed to be twice continuously Fr\\'echet differentiable w","authors_text":"Felix Lindner, Mih\\'aly Kov\\'acs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:08:05Z","title":"Weak error analysis via functional It\\^o calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08756","kind":"arxiv","version":2},"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":"sha256:2a7cff83332a56cc1880135ba05e5e989f11b9fa3855a68cb54d43fbe405d3ba","target":"record","created_at":"2026-05-18T01:12:29Z","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":"0c05f87e630e02cfc48b86d4c3bb20425df1dfaf1994e0a6cf28dfd72d2ca5d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:08:05Z","title_canon_sha256":"dfce4e33b41e654bc341b6668eedadb49b34ed2cafc0bb79d8ce937a830c14e1"},"schema_version":"1.0","source":{"id":"1603.08756","kind":"arxiv","version":2}},"canonical_sha256":"5ac9126fb4094c1c8e7de593117404060db9b0efb8c4271efa43b36573730b19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ac9126fb4094c1c8e7de593117404060db9b0efb8c4271efa43b36573730b19","first_computed_at":"2026-05-18T01:12:29.691335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:29.691335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zP/xpC3bi9P68tra4rQCj4btHK2jivKq3dLNB5Ds3ROKYREdZlpxwqpyEd+EybZsPjhdVqhn/jXFAWDotamTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:29.691690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a7cff83332a56cc1880135ba05e5e989f11b9fa3855a68cb54d43fbe405d3ba","sha256:331be73e97377356cce3d9d269f4db80e3ecbd7002b5301b4aa52f61c9acdd28"],"state_sha256":"555fdf16e5bc6fe5a1fe481e616a04ed834eae3d893e428b70a425d8b9b27cfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rgwr7djhQNjk2kyx5bx13O5CpBf5vva2ZyUj0UU0ADo8V1NKmdXTMmOjj3kyOmzqepesJALxHtUQhlBAIN/0DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T03:57:45.150833Z","bundle_sha256":"2b08224eb5f86a23a545eae6101ba1dd5c5d718f7fa0e1240ab1cf8728d865ec"}}