{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LBIRDPDPRLPTKXWLE2TXQUKITG","short_pith_number":"pith:LBIRDPDP","canonical_record":{"source":{"id":"1506.07686","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-25T10:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"836b9605b5d0793c7d2591764439f2a9cfa0479da082f72dfbfdd27ec0ffe5e9","abstract_canon_sha256":"f364da4379ae372dcaddabe6f769d3977c8bce28b644fc0adf8f6391d6580f1b"},"schema_version":"1.0"},"canonical_sha256":"585111bc6f8adf355ecb26a7785148998c8f7ef3e3b90fccd46177b411605b8f","source":{"kind":"arxiv","id":"1506.07686","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07686","created_at":"2026-05-18T00:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07686v2","created_at":"2026-05-18T00:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07686","created_at":"2026-05-18T00:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"LBIRDPDPRLPT","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBIRDPDPRLPTKXWL","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBIRDPDP","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LBIRDPDPRLPTKXWLE2TXQUKITG","target":"record","payload":{"canonical_record":{"source":{"id":"1506.07686","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-25T10:10:40Z","cross_cats_sorted":[],"title_canon_sha256":"836b9605b5d0793c7d2591764439f2a9cfa0479da082f72dfbfdd27ec0ffe5e9","abstract_canon_sha256":"f364da4379ae372dcaddabe6f769d3977c8bce28b644fc0adf8f6391d6580f1b"},"schema_version":"1.0"},"canonical_sha256":"585111bc6f8adf355ecb26a7785148998c8f7ef3e3b90fccd46177b411605b8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:00.322947Z","signature_b64":"WD7oG5aSIebAszxiB2aKyNW15kPIh+lRK4Nc6Fe5ggDvd7dXiK1lXpYNtHkWxgkXb9gpVlxem8cx/WU2EggPDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"585111bc6f8adf355ecb26a7785148998c8f7ef3e3b90fccd46177b411605b8f","last_reissued_at":"2026-05-18T00:34:00.322414Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:00.322414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.07686","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":"2026-05-18T00:34:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ecOB6Glo/Txq1ePnM5MMaY6RXRfbHQELF4+TKNoxisw8rSlWWnaiQ2wfcBdmRQbUI4fOMe48hI5y9fg4iOPNCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:05:46.693009Z"},"content_sha256":"e52539880a437953139d00282c4665f8bdc2db56b2d3a00488ccb0ff6e902cbd","schema_version":"1.0","event_id":"sha256:e52539880a437953139d00282c4665f8bdc2db56b2d3a00488ccb0ff6e902cbd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LBIRDPDPRLPTKXWLE2TXQUKITG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The exponential Lie series for continuous semimartingales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anke Wiese, Frederic Patras, Kurusch Ebrahimi-Fard, Simon J.A. Malham","submitted_at":"2015-06-25T10:10:40Z","abstract_excerpt":"We consider stochastic differential systems driven by continuous semimartingales and governed by non-commuting vector fields. We prove that the logarithm of the flowmap is an exponential Lie series. This relies on a natural change of basis to vector fields for the associated quadratic covariation processes, analogous to Stratonovich corrections. The flowmap can then be expanded as a series in compositional powers of vector fields and the logaritm of the flowmap can thus be expanded in the Lie algebra of vector fields. Further, we give a direct self-contained proof of the corresponding Chen-Str"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07686","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":"2026-05-18T00:34:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gK/OB/G0co79qd60QuyzFWrjoGzOil2bqbSYcSNWZsMI3zQUY46IXu23Oo69vn5AYmAlWYYVqA/X5cl6HZXCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T05:05:46.693773Z"},"content_sha256":"99eaef0d4ba04575a19e57ad4edfc352380b9263f0b70d3fb777832cee536a51","schema_version":"1.0","event_id":"sha256:99eaef0d4ba04575a19e57ad4edfc352380b9263f0b70d3fb777832cee536a51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBIRDPDPRLPTKXWLE2TXQUKITG/bundle.json","state_url":"https://pith.science/pith/LBIRDPDPRLPTKXWLE2TXQUKITG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBIRDPDPRLPTKXWLE2TXQUKITG/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":"2026-05-31T05:05:46Z","links":{"resolver":"https://pith.science/pith/LBIRDPDPRLPTKXWLE2TXQUKITG","bundle":"https://pith.science/pith/LBIRDPDPRLPTKXWLE2TXQUKITG/bundle.json","state":"https://pith.science/pith/LBIRDPDPRLPTKXWLE2TXQUKITG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBIRDPDPRLPTKXWLE2TXQUKITG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LBIRDPDPRLPTKXWLE2TXQUKITG","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":"f364da4379ae372dcaddabe6f769d3977c8bce28b644fc0adf8f6391d6580f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-25T10:10:40Z","title_canon_sha256":"836b9605b5d0793c7d2591764439f2a9cfa0479da082f72dfbfdd27ec0ffe5e9"},"schema_version":"1.0","source":{"id":"1506.07686","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.07686","created_at":"2026-05-18T00:34:00Z"},{"alias_kind":"arxiv_version","alias_value":"1506.07686v2","created_at":"2026-05-18T00:34:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.07686","created_at":"2026-05-18T00:34:00Z"},{"alias_kind":"pith_short_12","alias_value":"LBIRDPDPRLPT","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LBIRDPDPRLPTKXWL","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LBIRDPDP","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:99eaef0d4ba04575a19e57ad4edfc352380b9263f0b70d3fb777832cee536a51","target":"graph","created_at":"2026-05-18T00:34:00Z","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 stochastic differential systems driven by continuous semimartingales and governed by non-commuting vector fields. We prove that the logarithm of the flowmap is an exponential Lie series. This relies on a natural change of basis to vector fields for the associated quadratic covariation processes, analogous to Stratonovich corrections. The flowmap can then be expanded as a series in compositional powers of vector fields and the logaritm of the flowmap can thus be expanded in the Lie algebra of vector fields. Further, we give a direct self-contained proof of the corresponding Chen-Str","authors_text":"Anke Wiese, Frederic Patras, Kurusch Ebrahimi-Fard, Simon J.A. Malham","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-25T10:10:40Z","title":"The exponential Lie series for continuous semimartingales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.07686","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:e52539880a437953139d00282c4665f8bdc2db56b2d3a00488ccb0ff6e902cbd","target":"record","created_at":"2026-05-18T00:34:00Z","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":"f364da4379ae372dcaddabe6f769d3977c8bce28b644fc0adf8f6391d6580f1b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-25T10:10:40Z","title_canon_sha256":"836b9605b5d0793c7d2591764439f2a9cfa0479da082f72dfbfdd27ec0ffe5e9"},"schema_version":"1.0","source":{"id":"1506.07686","kind":"arxiv","version":2}},"canonical_sha256":"585111bc6f8adf355ecb26a7785148998c8f7ef3e3b90fccd46177b411605b8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"585111bc6f8adf355ecb26a7785148998c8f7ef3e3b90fccd46177b411605b8f","first_computed_at":"2026-05-18T00:34:00.322414Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:00.322414Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WD7oG5aSIebAszxiB2aKyNW15kPIh+lRK4Nc6Fe5ggDvd7dXiK1lXpYNtHkWxgkXb9gpVlxem8cx/WU2EggPDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:00.322947Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.07686","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e52539880a437953139d00282c4665f8bdc2db56b2d3a00488ccb0ff6e902cbd","sha256:99eaef0d4ba04575a19e57ad4edfc352380b9263f0b70d3fb777832cee536a51"],"state_sha256":"352b6e4dce4e2439a307482d6948d56b7cb8ac3d26ccefeca0284c9efdb730d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sJlVy+x0s+NNuEG14FeDw3zW+6d32VF7xJObhOSuhD00tKWuwHcUI0N98WJzM/sugXfKCz0y291OUMXQFSYJCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T05:05:46.698138Z","bundle_sha256":"720563fe82865bfbf884c69c0caff965e8bfeab33aa175426ac6dc355c6cc187"}}