{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2CTJWGAIAK73O2EPZL5S42CNL5","short_pith_number":"pith:2CTJWGAI","canonical_record":{"source":{"id":"1803.02655","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-07T14:04:50Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"da8f18373b9bb7a354e09c3daf5e9fbd849d27f6bfdc8d55e1b6ee88f310846a","abstract_canon_sha256":"f3254aeec560526e7031212e234ecc25a5231e2dec8ff6f72a0172548b2debef"},"schema_version":"1.0"},"canonical_sha256":"d0a69b180802bfb7688fcafb2e684d5f48bc060ac5ebe771baf9435aa75eb75b","source":{"kind":"arxiv","id":"1803.02655","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02655","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02655v4","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02655","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"2CTJWGAIAK73","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2CTJWGAIAK73O2EP","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2CTJWGAI","created_at":"2026-05-18T12:31:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2CTJWGAIAK73O2EPZL5S42CNL5","target":"record","payload":{"canonical_record":{"source":{"id":"1803.02655","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-07T14:04:50Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"da8f18373b9bb7a354e09c3daf5e9fbd849d27f6bfdc8d55e1b6ee88f310846a","abstract_canon_sha256":"f3254aeec560526e7031212e234ecc25a5231e2dec8ff6f72a0172548b2debef"},"schema_version":"1.0"},"canonical_sha256":"d0a69b180802bfb7688fcafb2e684d5f48bc060ac5ebe771baf9435aa75eb75b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:30.725340Z","signature_b64":"M3yyHnf4uyIgetBL8vo881rS97oI7Wk8Ax3LayuIJ/DY6DRkstuIVtC1LKbk8xSU1zvYAwF4kFLdBlJWesFjAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0a69b180802bfb7688fcafb2e684d5f48bc060ac5ebe771baf9435aa75eb75b","last_reissued_at":"2026-05-17T23:46:30.724743Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:30.724743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.02655","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5MRINhikqwmExXxg5ENm1DBhsZ/ZnpkzNaREMtPrTyoVv8/9A+i5i2n6rqqZR4lbGDm9fjvHKv9CykwZtw60AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T01:48:20.956467Z"},"content_sha256":"5145ba45e41ad61648eacbb8f005545f28ce3f3857ecfc18125b2e7b36f0ecdf","schema_version":"1.0","event_id":"sha256:5145ba45e41ad61648eacbb8f005545f28ce3f3857ecfc18125b2e7b36f0ecdf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2CTJWGAIAK73O2EPZL5S42CNL5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Law equivalence of Ornstein--Uhlenbeck processes driven by a L\\'evy process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Grzegorz Bartosz, Tomasz Kania","submitted_at":"2018-03-07T14:04:50Z","abstract_excerpt":"We demonstrate that two Ornstein--Uhlenbeck processes, that is, solutions to certain stochastic differential equations that are driven by a L\\'evy process L have equivalent laws as long as the eigenvalues of the covariance operator associated to the Wiener part of L are strictly positive. Moreover, we show that in the case where the underlying L\\'evy process is a purely jump process, which means that neither it has a Wiener part nor the drift, the absolute continuity of the law of one solution with respect to another forces equality of the solutions almost surely."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02655","kind":"arxiv","version":4},"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":"2026-05-17T23:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AchH/RPXrZojUqJzKimRJJi1L9yldJy5n7pnsLXFk6We2ZCuJ4XxyF5tY5pii75cJFVEynvucfVxkGCt48+ZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T01:48:20.956827Z"},"content_sha256":"35e0c31a8440d32a2970906de290bf178ffafb8632da35ae5eb2c7877202dfe0","schema_version":"1.0","event_id":"sha256:35e0c31a8440d32a2970906de290bf178ffafb8632da35ae5eb2c7877202dfe0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2CTJWGAIAK73O2EPZL5S42CNL5/bundle.json","state_url":"https://pith.science/pith/2CTJWGAIAK73O2EPZL5S42CNL5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2CTJWGAIAK73O2EPZL5S42CNL5/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":"2026-05-23T01:48:20Z","links":{"resolver":"https://pith.science/pith/2CTJWGAIAK73O2EPZL5S42CNL5","bundle":"https://pith.science/pith/2CTJWGAIAK73O2EPZL5S42CNL5/bundle.json","state":"https://pith.science/pith/2CTJWGAIAK73O2EPZL5S42CNL5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2CTJWGAIAK73O2EPZL5S42CNL5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2CTJWGAIAK73O2EPZL5S42CNL5","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":"f3254aeec560526e7031212e234ecc25a5231e2dec8ff6f72a0172548b2debef","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-07T14:04:50Z","title_canon_sha256":"da8f18373b9bb7a354e09c3daf5e9fbd849d27f6bfdc8d55e1b6ee88f310846a"},"schema_version":"1.0","source":{"id":"1803.02655","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.02655","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1803.02655v4","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.02655","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"2CTJWGAIAK73","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"2CTJWGAIAK73O2EP","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"2CTJWGAI","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:35e0c31a8440d32a2970906de290bf178ffafb8632da35ae5eb2c7877202dfe0","target":"graph","created_at":"2026-05-17T23:46:30Z","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 demonstrate that two Ornstein--Uhlenbeck processes, that is, solutions to certain stochastic differential equations that are driven by a L\\'evy process L have equivalent laws as long as the eigenvalues of the covariance operator associated to the Wiener part of L are strictly positive. Moreover, we show that in the case where the underlying L\\'evy process is a purely jump process, which means that neither it has a Wiener part nor the drift, the absolute continuity of the law of one solution with respect to another forces equality of the solutions almost surely.","authors_text":"Grzegorz Bartosz, Tomasz Kania","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-07T14:04:50Z","title":"Law equivalence of Ornstein--Uhlenbeck processes driven by a L\\'evy process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02655","kind":"arxiv","version":4},"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":"sha256:5145ba45e41ad61648eacbb8f005545f28ce3f3857ecfc18125b2e7b36f0ecdf","target":"record","created_at":"2026-05-17T23:46:30Z","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":"f3254aeec560526e7031212e234ecc25a5231e2dec8ff6f72a0172548b2debef","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-07T14:04:50Z","title_canon_sha256":"da8f18373b9bb7a354e09c3daf5e9fbd849d27f6bfdc8d55e1b6ee88f310846a"},"schema_version":"1.0","source":{"id":"1803.02655","kind":"arxiv","version":4}},"canonical_sha256":"d0a69b180802bfb7688fcafb2e684d5f48bc060ac5ebe771baf9435aa75eb75b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d0a69b180802bfb7688fcafb2e684d5f48bc060ac5ebe771baf9435aa75eb75b","first_computed_at":"2026-05-17T23:46:30.724743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:30.724743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M3yyHnf4uyIgetBL8vo881rS97oI7Wk8Ax3LayuIJ/DY6DRkstuIVtC1LKbk8xSU1zvYAwF4kFLdBlJWesFjAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:30.725340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.02655","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5145ba45e41ad61648eacbb8f005545f28ce3f3857ecfc18125b2e7b36f0ecdf","sha256:35e0c31a8440d32a2970906de290bf178ffafb8632da35ae5eb2c7877202dfe0"],"state_sha256":"addfd0167cf9a0cf5429429fd93125fd893d996f13a83c79196ac38089f7f17b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cRIORknBPasSgMQTvy7qSP13qWtscX5weK7dDNmq8Hoh2Ap4nJWS2RWlLtmIWGs+bcIFAJC0Cn6gQqzILUfaCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T01:48:20.958859Z","bundle_sha256":"2bc40b4dbcb9c70e73fecae5970e6448b371e232b1e037b8a2892c1b00846bc5"}}