{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XDXM7ZRATEVPTFQVL7QZZR5CH3","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":"ef3349944a4fd587d4803ff042f2fa858e2687c96867007f7c9f7c91c2e526c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-18T16:52:44Z","title_canon_sha256":"fdb2d3cde79f9a05b2164e4629f0069854281cca3782b949b0328e4abf84a399"},"schema_version":"1.0","source":{"id":"1411.4907","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4907","created_at":"2026-05-18T02:34:50Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4907v1","created_at":"2026-05-18T02:34:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4907","created_at":"2026-05-18T02:34:50Z"},{"alias_kind":"pith_short_12","alias_value":"XDXM7ZRATEVP","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XDXM7ZRATEVPTFQV","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XDXM7ZRA","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:440b0b7856b8561b0d88e89321617b86e5e6fc7945b1c6bbd90713b742af8e20","target":"graph","created_at":"2026-05-18T02:34:50Z","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":"The main objective of this work is to study a natural class of catalytic Ornstein-Uhlenbeck (O-U) processes with a measure-valued random catalyst, for example, super-Brownian motion. We relate this to the class of affine processes that provides a unified setting in which to view Ornstein-Uhlenbeck processes, superprocesses, and Ornstein-Uhlenbeck processes with superprocess catalyst. We then review some basic properties of super-Brownian motion which we need and introduce the Ornstein-Uhlenbeck process with catalyst given by a superprocess. The main results are the affine characterization of t","authors_text":"Donald A. Dawson, Juan-Manuel Perez-Abarca","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-18T16:52:44Z","title":"The catalytic Ornstein-Uhlenbeck process with superprocess catalyst"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4907","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":"sha256:072315bf9694904666e1b930c4bdbf27175e7c3d8698b80eaad856a341314df9","target":"record","created_at":"2026-05-18T02:34:50Z","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":"ef3349944a4fd587d4803ff042f2fa858e2687c96867007f7c9f7c91c2e526c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-11-18T16:52:44Z","title_canon_sha256":"fdb2d3cde79f9a05b2164e4629f0069854281cca3782b949b0328e4abf84a399"},"schema_version":"1.0","source":{"id":"1411.4907","kind":"arxiv","version":1}},"canonical_sha256":"b8eecfe620992af996155fe19cc7a23ecc4c2deac29b9bef8da84bf99ccc44fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8eecfe620992af996155fe19cc7a23ecc4c2deac29b9bef8da84bf99ccc44fe","first_computed_at":"2026-05-18T02:34:50.989868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:50.989868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ur+kIyQZv/fFVSxs4efYhogzWDp8Mhy1zvteq3Tz6ib0/GSLife7T7CawbekPHxnpbJ1TECb61GQD6mKo9uSCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:50.990249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4907","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:072315bf9694904666e1b930c4bdbf27175e7c3d8698b80eaad856a341314df9","sha256:440b0b7856b8561b0d88e89321617b86e5e6fc7945b1c6bbd90713b742af8e20"],"state_sha256":"a3cf8aef503cda325bba0b7f81b2c0b35fb12a5c93507d075134f938fa4982c3"}