{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:EKTHOXPY4B2NEX6NYIGHA36TEJ","short_pith_number":"pith:EKTHOXPY","canonical_record":{"source":{"id":"1608.05362","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-18T18:25:24Z","cross_cats_sorted":[],"title_canon_sha256":"886b72a2520f47222450e2974d44578f6153ae76bda820fe21d7288e95ca1d27","abstract_canon_sha256":"c93066e20824c53ceee74b75146691487470c6ecdce844126f77aafa08962280"},"schema_version":"1.0"},"canonical_sha256":"22a6775df8e074d25fcdc20c706fd32240382ff09283ae286fabb77b746f3ef0","source":{"kind":"arxiv","id":"1608.05362","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05362","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05362v3","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05362","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"EKTHOXPY4B2N","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EKTHOXPY4B2NEX6N","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EKTHOXPY","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:EKTHOXPY4B2NEX6NYIGHA36TEJ","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05362","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-18T18:25:24Z","cross_cats_sorted":[],"title_canon_sha256":"886b72a2520f47222450e2974d44578f6153ae76bda820fe21d7288e95ca1d27","abstract_canon_sha256":"c93066e20824c53ceee74b75146691487470c6ecdce844126f77aafa08962280"},"schema_version":"1.0"},"canonical_sha256":"22a6775df8e074d25fcdc20c706fd32240382ff09283ae286fabb77b746f3ef0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:49.481424Z","signature_b64":"2lHQj+gtzSaZ6RUQUSfanlihE8rOv4ZPYK2iBZUfnoyem4RjF2Ie/2tfqEUetlY/12pO6Ai4r80q6Sirs9ihCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22a6775df8e074d25fcdc20c706fd32240382ff09283ae286fabb77b746f3ef0","last_reissued_at":"2026-05-18T01:04:49.481043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:49.481043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05362","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":"2026-05-18T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bzFz34uidJZGaFwogJ5mPoFmStfKWb7zHogFewT995V6qodT50wWi80DEKZgzveLX9T7jDCNLilL1+r5oUXgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:58:52.462051Z"},"content_sha256":"14ab442186b512305dea6f8cbe674d37102e18b2a701c9a457767caf9145f5f3","schema_version":"1.0","event_id":"sha256:14ab442186b512305dea6f8cbe674d37102e18b2a701c9a457767caf9145f5f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:EKTHOXPY4B2NEX6NYIGHA36TEJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On explicit solutions to Ito diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bruno Remillard, Michael A. Kouritzin","submitted_at":"2016-08-18T18:25:24Z","abstract_excerpt":"Strong solutions of p-dimensional stochastic differential equations that can be represented locally in explicit simulation form are considered. The following three-way equivalence is established: 1) There exists such a representation from all starting points, 2) the representation pair satisfies a set differential equations, and 3) the stochastic differential equation coefficients satisfy commutation relations. Next, construction theorems, based on a diffeomorphism between the original equation solutions and the strong solutions to a simpler Ito integral equation, with a possible deterministic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05362","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":"2026-05-18T01:04:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0MPPz+vSWRZ4RvGVBfnXF1izWxhBi1IlTFt/erFG805VsOQRLju2pJ36mBBYE8YdkWL3GS2LvUTYy5YPM+iGBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:58:52.462400Z"},"content_sha256":"baf86591ee26790c587d1d5f1a376f9a8609903a961eeaecb9caa8d92331ebd3","schema_version":"1.0","event_id":"sha256:baf86591ee26790c587d1d5f1a376f9a8609903a961eeaecb9caa8d92331ebd3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EKTHOXPY4B2NEX6NYIGHA36TEJ/bundle.json","state_url":"https://pith.science/pith/EKTHOXPY4B2NEX6NYIGHA36TEJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EKTHOXPY4B2NEX6NYIGHA36TEJ/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":"2026-06-22T09:58:52Z","links":{"resolver":"https://pith.science/pith/EKTHOXPY4B2NEX6NYIGHA36TEJ","bundle":"https://pith.science/pith/EKTHOXPY4B2NEX6NYIGHA36TEJ/bundle.json","state":"https://pith.science/pith/EKTHOXPY4B2NEX6NYIGHA36TEJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EKTHOXPY4B2NEX6NYIGHA36TEJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:EKTHOXPY4B2NEX6NYIGHA36TEJ","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":"c93066e20824c53ceee74b75146691487470c6ecdce844126f77aafa08962280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-18T18:25:24Z","title_canon_sha256":"886b72a2520f47222450e2974d44578f6153ae76bda820fe21d7288e95ca1d27"},"schema_version":"1.0","source":{"id":"1608.05362","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05362","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05362v3","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05362","created_at":"2026-05-18T01:04:49Z"},{"alias_kind":"pith_short_12","alias_value":"EKTHOXPY4B2N","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"EKTHOXPY4B2NEX6N","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"EKTHOXPY","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:baf86591ee26790c587d1d5f1a376f9a8609903a961eeaecb9caa8d92331ebd3","target":"graph","created_at":"2026-05-18T01:04:49Z","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":"Strong solutions of p-dimensional stochastic differential equations that can be represented locally in explicit simulation form are considered. The following three-way equivalence is established: 1) There exists such a representation from all starting points, 2) the representation pair satisfies a set differential equations, and 3) the stochastic differential equation coefficients satisfy commutation relations. Next, construction theorems, based on a diffeomorphism between the original equation solutions and the strong solutions to a simpler Ito integral equation, with a possible deterministic","authors_text":"Bruno Remillard, Michael A. Kouritzin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-18T18:25:24Z","title":"On explicit solutions to Ito diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05362","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":"sha256:14ab442186b512305dea6f8cbe674d37102e18b2a701c9a457767caf9145f5f3","target":"record","created_at":"2026-05-18T01:04:49Z","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":"c93066e20824c53ceee74b75146691487470c6ecdce844126f77aafa08962280","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-18T18:25:24Z","title_canon_sha256":"886b72a2520f47222450e2974d44578f6153ae76bda820fe21d7288e95ca1d27"},"schema_version":"1.0","source":{"id":"1608.05362","kind":"arxiv","version":3}},"canonical_sha256":"22a6775df8e074d25fcdc20c706fd32240382ff09283ae286fabb77b746f3ef0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22a6775df8e074d25fcdc20c706fd32240382ff09283ae286fabb77b746f3ef0","first_computed_at":"2026-05-18T01:04:49.481043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:49.481043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2lHQj+gtzSaZ6RUQUSfanlihE8rOv4ZPYK2iBZUfnoyem4RjF2Ie/2tfqEUetlY/12pO6Ai4r80q6Sirs9ihCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:49.481424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05362","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:14ab442186b512305dea6f8cbe674d37102e18b2a701c9a457767caf9145f5f3","sha256:baf86591ee26790c587d1d5f1a376f9a8609903a961eeaecb9caa8d92331ebd3"],"state_sha256":"51b3e363fefcd86fd57ae115bd642957e6308c978a4cab9b9455932fd72e5b88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YzUM4Zgz9OskzYazS2JFVRAsE2Tz3LWdPeSWwdX95YrqVttdAitpX6HfaNIGzEKXSblYd6pI7AiD6LTH1E0/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:58:52.464221Z","bundle_sha256":"8e9068543e96e37336b874b55a239e41fc8ebf768a5b6baf91e6da5262ebc2dc"}}