{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RZXKMB24R2W7AC7TW55K6BZUFH","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":"f856633752a4b6f202d7613ff3e190c6aadb3252c931b5c5bc40fea381fd4002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-30T09:01:46Z","title_canon_sha256":"3f6cd24b83de778dffdeadefd64bfac31a3bea1866810275ebefaa7f24ceec99"},"schema_version":"1.0","source":{"id":"1309.7761","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.7761","created_at":"2026-05-18T01:47:24Z"},{"alias_kind":"arxiv_version","alias_value":"1309.7761v1","created_at":"2026-05-18T01:47:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7761","created_at":"2026-05-18T01:47:24Z"},{"alias_kind":"pith_short_12","alias_value":"RZXKMB24R2W7","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RZXKMB24R2W7AC7T","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RZXKMB24","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:3a44ee39e6b64d3a3edc2ca2690b15f4a902353f9906e628e765ec99d19f92a1","target":"graph","created_at":"2026-05-18T01:47:24Z","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":"In this paper we study the conditional limit theorems for critical continuous-state branching processes with branching mechanism $\\psi(\\lambda)=\\lambda^{1+\\alpha}L(1/\\lambda)$ where $\\alpha\\in [0,1]$ and $L$ is slowly varying at $\\infty$. We prove that if $\\alpha\\in (0,1]$, there are norming constants $Q_{t}\\to 0$ (as $t\\uparrow +\\infty$) such that for every $x>0$, $P_{x}\\left(Q_{t}X_{t}\\in\\cdot|X_{t}>0\\right)$ converges weakly to a non-degenerate limit. The converse assertion is also true provided the regularity of $\\psi$ at 0. We give a conditional limit theorem for the case $\\alpha=0$. The ","authors_text":"Guo-Huan Zhao, Ting Yang, Yan-Xia Ren","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-30T09:01:46Z","title":"Conditional limit theorems for critical continuous-state branching processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7761","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":"sha256:5c5cb7ea478717fecb54743c1638f6bb455d2d7dbfdb6fe00cc31f4d818cd4bd","target":"record","created_at":"2026-05-18T01:47:24Z","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":"f856633752a4b6f202d7613ff3e190c6aadb3252c931b5c5bc40fea381fd4002","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-30T09:01:46Z","title_canon_sha256":"3f6cd24b83de778dffdeadefd64bfac31a3bea1866810275ebefaa7f24ceec99"},"schema_version":"1.0","source":{"id":"1309.7761","kind":"arxiv","version":1}},"canonical_sha256":"8e6ea6075c8eadf00bf3b77aaf073429f57021bebd49614d110a5b256e3681e5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e6ea6075c8eadf00bf3b77aaf073429f57021bebd49614d110a5b256e3681e5","first_computed_at":"2026-05-18T01:47:24.610850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:47:24.610850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KBKSrv4PVSEoyCjbqZn7sEDZgZaDcdskNGW5dNytJrPeW5LOAqRKHxaU+MvtCe2ybR7CKt3tE3I2X4vJg3m0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:47:24.611543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.7761","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c5cb7ea478717fecb54743c1638f6bb455d2d7dbfdb6fe00cc31f4d818cd4bd","sha256:3a44ee39e6b64d3a3edc2ca2690b15f4a902353f9906e628e765ec99d19f92a1"],"state_sha256":"f062b8bfcf156d663ae8660b07bb9a06f27d671ac5a5a967d32173b8df88b3bc"}