{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:ZQPHV72CHUJBDZUWHPUMOBH2B3","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":"d899e536124f9d3b202a3711481dcf025cad6172d816ae2dedef80e7b051a57b","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2005-04-19T15:55:36Z","title_canon_sha256":"0d77b8d8313177457e0c76b32ccc5d8cf97f4744eb67dd2c928a5e8ec9de8e64"},"schema_version":"1.0","source":{"id":"math/0504391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0504391","created_at":"2026-05-18T01:38:25Z"},{"alias_kind":"arxiv_version","alias_value":"math/0504391v1","created_at":"2026-05-18T01:38:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0504391","created_at":"2026-05-18T01:38:25Z"},{"alias_kind":"pith_short_12","alias_value":"ZQPHV72CHUJB","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZQPHV72CHUJBDZUW","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZQPHV72C","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:9f183ab7a7f54a9adb4be6f902d02b55bdeabf065fa8ca98898d4fdf1d863c1b","target":"graph","created_at":"2026-05-18T01:38:25Z","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 purpose of this article is to give a rather thorough understanding of the compact support property for measure-valued processes corresponding to semi-linear equations of the form \\[ \\begin{aligned}& u_t=Lu+\\beta u-\\alpha u^p \\text{in} R^d\\times (0,\\infty), p\\in(1,2]; &u(x,0)=f(x) \\text{in} R^d; &u(x,t)\\ge0 \\text{in} R^d\\times[0,\\infty). \\end{aligned} \\] In particular, we shall investigate how the interplay between the underlying motion (the diffusion process corresponding to $L$) and the branching affects the compact support property. In \\cite{EP99}, the compact support property was shown ","authors_text":"Janos Englander, Ross G. Pinsky","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2005-04-19T15:55:36Z","title":"The compact support property for measure-valued processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0504391","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:c820956b07f5da55f1a48ad26bd8f125b9abc6a5db05c92e81fa5c4a215b224f","target":"record","created_at":"2026-05-18T01:38:25Z","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":"d899e536124f9d3b202a3711481dcf025cad6172d816ae2dedef80e7b051a57b","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2005-04-19T15:55:36Z","title_canon_sha256":"0d77b8d8313177457e0c76b32ccc5d8cf97f4744eb67dd2c928a5e8ec9de8e64"},"schema_version":"1.0","source":{"id":"math/0504391","kind":"arxiv","version":1}},"canonical_sha256":"cc1e7aff423d1211e6963be8c704fa0ee4e701ecee04600d4de005cdf7175227","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc1e7aff423d1211e6963be8c704fa0ee4e701ecee04600d4de005cdf7175227","first_computed_at":"2026-05-18T01:38:25.045982Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:25.045982Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qYGf/BZM4+YJ2APU7uO8DT+NDoUasF0btUqt2+CPro643jX6Q7Nm8c/LQmf9pTDWWhQA26psL3oQWTeV0XviCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:25.046733Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0504391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c820956b07f5da55f1a48ad26bd8f125b9abc6a5db05c92e81fa5c4a215b224f","sha256:9f183ab7a7f54a9adb4be6f902d02b55bdeabf065fa8ca98898d4fdf1d863c1b"],"state_sha256":"6004fff257eab995e79434c07ed68242e47ddf9a1840af1fc0b12424e3e8e4de"}