{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:HXIZY7HGWZ6OZ662MIS3W2YTS6","short_pith_number":"pith:HXIZY7HG","schema_version":"1.0","canonical_sha256":"3dd19c7ce6b67cecfbda6225bb6b1397bfd5d07279da67026bfd9353ff002507","source":{"kind":"arxiv","id":"1004.1426","version":3},"attestation_state":"computed","paper":{"title":"The number of absorbed individuals in branching Brownian motion with a barrier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pascal Maillard","submitted_at":"2010-04-08T20:50:50Z","abstract_excerpt":"We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift $c$. At the point $x > 0$, we add an absorbing barrier, i.e.\\ individuals touching the barrier are instantly killed without producing offspring. It is known that there is a critical drift $c_0$, such that this process becomes extinct almost surely if and only if $c \\ge c_0$. In this case, if $Z_x$ denotes the number of individuals absorbed at the barrier, we give an asymptotic for $P(Z_x=n)$ as $n$ goes to infinity. If $c=c_0$ and the reproduction is deterministic, this improves upo"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1004.1426","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-08T20:50:50Z","cross_cats_sorted":[],"title_canon_sha256":"7e0e90939917277aaa29716dfb26ff48f0a495f1a0b1736ffe8e8fef035d9625","abstract_canon_sha256":"eee5e966d8a7f8789ce991d448a9dbe662bb50643c7f2a775ab1b22dde478bb3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:13.958419Z","signature_b64":"IQ/ttlcwZ7X3/S9BgEw3kjxTDSCqysp3KUoGAGuniIH3ga53scccXF/5IrHLNPuzgsSaX+11XB7ftZwfV44BCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3dd19c7ce6b67cecfbda6225bb6b1397bfd5d07279da67026bfd9353ff002507","last_reissued_at":"2026-05-18T03:06:13.957884Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:13.957884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The number of absorbed individuals in branching Brownian motion with a barrier","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Pascal Maillard","submitted_at":"2010-04-08T20:50:50Z","abstract_excerpt":"We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift $c$. At the point $x > 0$, we add an absorbing barrier, i.e.\\ individuals touching the barrier are instantly killed without producing offspring. It is known that there is a critical drift $c_0$, such that this process becomes extinct almost surely if and only if $c \\ge c_0$. In this case, if $Z_x$ denotes the number of individuals absorbed at the barrier, we give an asymptotic for $P(Z_x=n)$ as $n$ goes to infinity. If $c=c_0$ and the reproduction is deterministic, this improves upo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1426","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1004.1426","created_at":"2026-05-18T03:06:13.957967+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.1426v3","created_at":"2026-05-18T03:06:13.957967+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1426","created_at":"2026-05-18T03:06:13.957967+00:00"},{"alias_kind":"pith_short_12","alias_value":"HXIZY7HGWZ6O","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"HXIZY7HGWZ6OZ662","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"HXIZY7HG","created_at":"2026-05-18T12:26:07.630475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HXIZY7HGWZ6OZ662MIS3W2YTS6","json":"https://pith.science/pith/HXIZY7HGWZ6OZ662MIS3W2YTS6.json","graph_json":"https://pith.science/api/pith-number/HXIZY7HGWZ6OZ662MIS3W2YTS6/graph.json","events_json":"https://pith.science/api/pith-number/HXIZY7HGWZ6OZ662MIS3W2YTS6/events.json","paper":"https://pith.science/paper/HXIZY7HG"},"agent_actions":{"view_html":"https://pith.science/pith/HXIZY7HGWZ6OZ662MIS3W2YTS6","download_json":"https://pith.science/pith/HXIZY7HGWZ6OZ662MIS3W2YTS6.json","view_paper":"https://pith.science/paper/HXIZY7HG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.1426&json=true","fetch_graph":"https://pith.science/api/pith-number/HXIZY7HGWZ6OZ662MIS3W2YTS6/graph.json","fetch_events":"https://pith.science/api/pith-number/HXIZY7HGWZ6OZ662MIS3W2YTS6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HXIZY7HGWZ6OZ662MIS3W2YTS6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HXIZY7HGWZ6OZ662MIS3W2YTS6/action/storage_attestation","attest_author":"https://pith.science/pith/HXIZY7HGWZ6OZ662MIS3W2YTS6/action/author_attestation","sign_citation":"https://pith.science/pith/HXIZY7HGWZ6OZ662MIS3W2YTS6/action/citation_signature","submit_replication":"https://pith.science/pith/HXIZY7HGWZ6OZ662MIS3W2YTS6/action/replication_record"}},"created_at":"2026-05-18T03:06:13.957967+00:00","updated_at":"2026-05-18T03:06:13.957967+00:00"}