{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DGNF2TIIQOTZEQU365346VILZ7","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":"d69930a43af99f31cc7b7ba383045ef5e8813786b5e944d30665b8e7a0efda46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-16T09:19:22Z","title_canon_sha256":"1af515b65d8e18f90f0a8200d3a1d6d12b77f0984f2bfa10473c9eab8c925d68"},"schema_version":"1.0","source":{"id":"1410.4344","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4344","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4344v2","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4344","created_at":"2026-05-18T01:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"DGNF2TIIQOTZ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DGNF2TIIQOTZEQU3","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DGNF2TII","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:9af257133a0b1737617891eceb3018927c5150aea6d27cadbde65373978b5500","target":"graph","created_at":"2026-05-18T01:33:24Z","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":"We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat equation and predicts that starting from the empty configuration the total number of particles grows as $c \\sqrt{t} \\log t$. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.","authors_text":"Matthias Birkner, Rongfeng Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-16T09:19:22Z","title":"One-dimensional random walks with self-blocking immigration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4344","kind":"arxiv","version":2},"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":"sha256:82a1fddf1244d633fd20c9db27b428ac12817bc26ceb94058af94799701ca3e4","target":"record","created_at":"2026-05-18T01:33:24Z","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":"d69930a43af99f31cc7b7ba383045ef5e8813786b5e944d30665b8e7a0efda46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-16T09:19:22Z","title_canon_sha256":"1af515b65d8e18f90f0a8200d3a1d6d12b77f0984f2bfa10473c9eab8c925d68"},"schema_version":"1.0","source":{"id":"1410.4344","kind":"arxiv","version":2}},"canonical_sha256":"199a5d4d0883a792429bf777cf550bcfd8cbeab7ce2d8eeb72349e65c7ee2393","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"199a5d4d0883a792429bf777cf550bcfd8cbeab7ce2d8eeb72349e65c7ee2393","first_computed_at":"2026-05-18T01:33:24.333576Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:24.333576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jkzk41LjwhV8hXhBTjaQdDICjpyFuK1ZespXD8ceYCAihONUhdZXOy0fjwKnISFFEfVH0ACBgpnW6gs3f10iDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:24.334227Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4344","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82a1fddf1244d633fd20c9db27b428ac12817bc26ceb94058af94799701ca3e4","sha256:9af257133a0b1737617891eceb3018927c5150aea6d27cadbde65373978b5500"],"state_sha256":"222a393e1b66bde4ecc826e5124da9ccdbfe515e5f0c6bd467d32bbf6897a2e0"}