{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:26HQTX5OMBZKDA4SAPJDGCVGTM","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":"90bb40967595884dd2f0be73dc32ff637c14553c2e1ceafe9cdbbfd69ef4b99d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-05T22:03:46Z","title_canon_sha256":"4d926a9678114096dfa3cb1dca6ff7a2654340fd139fdc75eaaea4acabff5f52"},"schema_version":"1.0","source":{"id":"1612.01573","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.01573","created_at":"2026-05-18T00:55:48Z"},{"alias_kind":"arxiv_version","alias_value":"1612.01573v1","created_at":"2026-05-18T00:55:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.01573","created_at":"2026-05-18T00:55:48Z"},{"alias_kind":"pith_short_12","alias_value":"26HQTX5OMBZK","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"26HQTX5OMBZKDA4S","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"26HQTX5O","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:51a1e0fb9b38951983650557d7df193fb388e1c06705c91b6255eea542d232ed","target":"graph","created_at":"2026-05-18T00:55:48Z","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 prove weak convergence on the Skorokhod space of Galton-Watson processes with immigration, properly normalized, under the assumption that the tail of the immigration distribution has a logarithmic decay. The limits are extremal shot noise processes. By considering marginal distributions, we recover the results of Pakes [Adv. Appl. Probab., 11(1979), 31--62].","authors_text":"Alexander Iksanov, Zakhar Kabluchko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-05T22:03:46Z","title":"Functional limit theorems for Galton-Watson processes with very active immigration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01573","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":"sha256:6f93bf91074eeaccc8f08b2b74936a26121dc82c6309779f84873007295a89c0","target":"record","created_at":"2026-05-18T00:55:48Z","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":"90bb40967595884dd2f0be73dc32ff637c14553c2e1ceafe9cdbbfd69ef4b99d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-12-05T22:03:46Z","title_canon_sha256":"4d926a9678114096dfa3cb1dca6ff7a2654340fd139fdc75eaaea4acabff5f52"},"schema_version":"1.0","source":{"id":"1612.01573","kind":"arxiv","version":1}},"canonical_sha256":"d78f09dfae6072a1839203d2330aa69b03e611a351193f94138e5bcda839bc18","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d78f09dfae6072a1839203d2330aa69b03e611a351193f94138e5bcda839bc18","first_computed_at":"2026-05-18T00:55:48.158097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:48.158097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e/HJxP247X+sGQCS8NztjOfGvtwsMTusIeVBtqQj3ZJkQxZgqxnRvKVzLs0WJwcbqG9tQUonGEjoBYZGGv54Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:48.158657Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.01573","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f93bf91074eeaccc8f08b2b74936a26121dc82c6309779f84873007295a89c0","sha256:51a1e0fb9b38951983650557d7df193fb388e1c06705c91b6255eea542d232ed"],"state_sha256":"b785dd476025fc0f0180e4b8a7309485876e7a39244794a5bf9292bcde4cf112"}