{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VQ2QNH7PTV7WUVBVDZZXXSCNXZ","short_pith_number":"pith:VQ2QNH7P","canonical_record":{"source":{"id":"1411.2752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-11T10:23:27Z","cross_cats_sorted":[],"title_canon_sha256":"aedd687494acc918f55dece15591615821d925eeaaee71d4eceae8ab2b4b9d73","abstract_canon_sha256":"332b28090cc7700f6000aadae06b19f6f7499c1ac701cad0d4f794c12052b4f8"},"schema_version":"1.0"},"canonical_sha256":"ac35069fef9d7f6a54351e737bc84dbe5f6d80d492cc9f85057a9454cbae2ec8","source":{"kind":"arxiv","id":"1411.2752","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2752","created_at":"2026-05-18T02:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2752v1","created_at":"2026-05-18T02:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2752","created_at":"2026-05-18T02:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"VQ2QNH7PTV7W","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VQ2QNH7PTV7WUVBV","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VQ2QNH7P","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VQ2QNH7PTV7WUVBVDZZXXSCNXZ","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2752","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-11T10:23:27Z","cross_cats_sorted":[],"title_canon_sha256":"aedd687494acc918f55dece15591615821d925eeaaee71d4eceae8ab2b4b9d73","abstract_canon_sha256":"332b28090cc7700f6000aadae06b19f6f7499c1ac701cad0d4f794c12052b4f8"},"schema_version":"1.0"},"canonical_sha256":"ac35069fef9d7f6a54351e737bc84dbe5f6d80d492cc9f85057a9454cbae2ec8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:53.156402Z","signature_b64":"fcRazweOoUDJ0dAi2d4JtT0R7XvO+nWjY+DL6mOJJawfGXgWO203vdfRuSC/+cr4i++M3XpYQNGLc/FDM2J5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac35069fef9d7f6a54351e737bc84dbe5f6d80d492cc9f85057a9454cbae2ec8","last_reissued_at":"2026-05-18T02:37:53.155907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:53.155907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2752","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":"2026-05-18T02:37:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dnMqFZW8l4KLKEdNLnBVeGowQD+THwtXwwxN3oyWim1SfTuzvSRzHIr/eKp5PTCVtLn+VDQV00MMhDVNDPOpAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:55:27.700570Z"},"content_sha256":"b7e01d1006190243677e52f987b79217c575cd086ef88d78a38a2d893a453b57","schema_version":"1.0","event_id":"sha256:b7e01d1006190243677e52f987b79217c575cd086ef88d78a38a2d893a453b57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VQ2QNH7PTV7WUVBVDZZXXSCNXZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Infinite Dimensional Ornstein-Uhlenbeck Processes Driven by Levy Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Applebaum","submitted_at":"2014-11-11T10:23:27Z","abstract_excerpt":"We review the probabilistic properties of Ornstein-Uhlenbeck processes in Hilbert spaces driven by L\\'{e}vy processes. The emphasis is on the different contexts in which these processes arise, such as stochastic partial differential equations, continuous-state branching processes, generalised Mehler semigroups and operator self-decomposable distributions. We also examine generalisations to the case where the driving noise is cylindrical."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2752","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":"2026-05-18T02:37:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pO6tLoimsm+9eRQPD03h3OcS08g0t9PbYegQLzkqm0SlYXZ2GLXJA5oe0X8Red1rgvTTbIkMeiDrNlGbCGyrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:55:27.700906Z"},"content_sha256":"eafed4d86efcfc941a2db9f8f38b9cfe69d02ffcdd526019ac1219933e2b31e9","schema_version":"1.0","event_id":"sha256:eafed4d86efcfc941a2db9f8f38b9cfe69d02ffcdd526019ac1219933e2b31e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VQ2QNH7PTV7WUVBVDZZXXSCNXZ/bundle.json","state_url":"https://pith.science/pith/VQ2QNH7PTV7WUVBVDZZXXSCNXZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VQ2QNH7PTV7WUVBVDZZXXSCNXZ/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":"2026-06-27T10:55:27Z","links":{"resolver":"https://pith.science/pith/VQ2QNH7PTV7WUVBVDZZXXSCNXZ","bundle":"https://pith.science/pith/VQ2QNH7PTV7WUVBVDZZXXSCNXZ/bundle.json","state":"https://pith.science/pith/VQ2QNH7PTV7WUVBVDZZXXSCNXZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VQ2QNH7PTV7WUVBVDZZXXSCNXZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VQ2QNH7PTV7WUVBVDZZXXSCNXZ","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":"332b28090cc7700f6000aadae06b19f6f7499c1ac701cad0d4f794c12052b4f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-11T10:23:27Z","title_canon_sha256":"aedd687494acc918f55dece15591615821d925eeaaee71d4eceae8ab2b4b9d73"},"schema_version":"1.0","source":{"id":"1411.2752","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2752","created_at":"2026-05-18T02:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2752v1","created_at":"2026-05-18T02:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2752","created_at":"2026-05-18T02:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"VQ2QNH7PTV7W","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VQ2QNH7PTV7WUVBV","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VQ2QNH7P","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:eafed4d86efcfc941a2db9f8f38b9cfe69d02ffcdd526019ac1219933e2b31e9","target":"graph","created_at":"2026-05-18T02:37:53Z","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 review the probabilistic properties of Ornstein-Uhlenbeck processes in Hilbert spaces driven by L\\'{e}vy processes. The emphasis is on the different contexts in which these processes arise, such as stochastic partial differential equations, continuous-state branching processes, generalised Mehler semigroups and operator self-decomposable distributions. We also examine generalisations to the case where the driving noise is cylindrical.","authors_text":"David Applebaum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-11T10:23:27Z","title":"Infinite Dimensional Ornstein-Uhlenbeck Processes Driven by Levy Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2752","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:b7e01d1006190243677e52f987b79217c575cd086ef88d78a38a2d893a453b57","target":"record","created_at":"2026-05-18T02:37:53Z","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":"332b28090cc7700f6000aadae06b19f6f7499c1ac701cad0d4f794c12052b4f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-11T10:23:27Z","title_canon_sha256":"aedd687494acc918f55dece15591615821d925eeaaee71d4eceae8ab2b4b9d73"},"schema_version":"1.0","source":{"id":"1411.2752","kind":"arxiv","version":1}},"canonical_sha256":"ac35069fef9d7f6a54351e737bc84dbe5f6d80d492cc9f85057a9454cbae2ec8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac35069fef9d7f6a54351e737bc84dbe5f6d80d492cc9f85057a9454cbae2ec8","first_computed_at":"2026-05-18T02:37:53.155907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:53.155907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fcRazweOoUDJ0dAi2d4JtT0R7XvO+nWjY+DL6mOJJawfGXgWO203vdfRuSC/+cr4i++M3XpYQNGLc/FDM2J5Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:53.156402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2752","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7e01d1006190243677e52f987b79217c575cd086ef88d78a38a2d893a453b57","sha256:eafed4d86efcfc941a2db9f8f38b9cfe69d02ffcdd526019ac1219933e2b31e9"],"state_sha256":"3ac8f14d99c864c1efef773880613666d8e46838c676aa1e5f776bf8a07ea463"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qvw7RslX4j1/zlneqpH/X9KmY7bKxP9LZewBikknB8tOdYDTtPO9WLsCyA3284mudEv04hPuw68O4aUaiTH8BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:55:27.702710Z","bundle_sha256":"d58b7b6065d6263901f5a5546c1ae5d6108f706113f9680be8f6f2a20d1aaa81"}}