{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:YKPSZ3JIMECAT2NNPXHSVPGJF7","short_pith_number":"pith:YKPSZ3JI","schema_version":"1.0","canonical_sha256":"c29f2ced28610409e9ad7dcf2abcc92fe6ad87fc199178afa7f4819f541fc0ba","source":{"kind":"arxiv","id":"1605.03069","version":3},"attestation_state":"computed","paper":{"title":"A pathwise iterative approach to the extinction of branching processes with countably many types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Geoffrey Decrouez, Peter Braunsteins, Sophie Hautphenne","submitted_at":"2016-05-10T15:50:09Z","abstract_excerpt":"We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but increasing sets of types. A pathwise approach is then used to show that, under some sufficient conditions, the corresponding sequence of extinction probability vectors converges to the global extinction probability vector of the Galton-Watson processes with countably infinitely many types. This gives rise to a number of iterative methods for the computation of the global extinction probability vector."},"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":"1605.03069","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-10T15:50:09Z","cross_cats_sorted":[],"title_canon_sha256":"62e1ea4a945ec5023dc8cb339d82d40843bb92a9be5a06f1ea59147dd2c25874","abstract_canon_sha256":"b08c18458fa67bd3e58567d7225c84db64937f5236c4f85a69ebc43302e3b588"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:02.770408Z","signature_b64":"XH+kXHzh0nWY9qAfKszQA7T3OL0KzDGXrysuTcKlAbj+0LqqcpwPfD6s+S+elpc07EuH67AJ6yBoIZcyInz/Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c29f2ced28610409e9ad7dcf2abcc92fe6ad87fc199178afa7f4819f541fc0ba","last_reissued_at":"2026-05-18T00:28:02.769907Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:02.769907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A pathwise iterative approach to the extinction of branching processes with countably many types","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Geoffrey Decrouez, Peter Braunsteins, Sophie Hautphenne","submitted_at":"2016-05-10T15:50:09Z","abstract_excerpt":"We consider the extinction events of Galton-Watson processes with countably infinitely many types. In particular, we construct truncated and augmented Galton-Watson processes with finite but increasing sets of types. A pathwise approach is then used to show that, under some sufficient conditions, the corresponding sequence of extinction probability vectors converges to the global extinction probability vector of the Galton-Watson processes with countably infinitely many types. This gives rise to a number of iterative methods for the computation of the global extinction probability vector."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.03069","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":"1605.03069","created_at":"2026-05-18T00:28:02.769975+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.03069v3","created_at":"2026-05-18T00:28:02.769975+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.03069","created_at":"2026-05-18T00:28:02.769975+00:00"},{"alias_kind":"pith_short_12","alias_value":"YKPSZ3JIMECA","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"YKPSZ3JIMECAT2NN","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"YKPSZ3JI","created_at":"2026-05-18T12:30:53.716459+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/YKPSZ3JIMECAT2NNPXHSVPGJF7","json":"https://pith.science/pith/YKPSZ3JIMECAT2NNPXHSVPGJF7.json","graph_json":"https://pith.science/api/pith-number/YKPSZ3JIMECAT2NNPXHSVPGJF7/graph.json","events_json":"https://pith.science/api/pith-number/YKPSZ3JIMECAT2NNPXHSVPGJF7/events.json","paper":"https://pith.science/paper/YKPSZ3JI"},"agent_actions":{"view_html":"https://pith.science/pith/YKPSZ3JIMECAT2NNPXHSVPGJF7","download_json":"https://pith.science/pith/YKPSZ3JIMECAT2NNPXHSVPGJF7.json","view_paper":"https://pith.science/paper/YKPSZ3JI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.03069&json=true","fetch_graph":"https://pith.science/api/pith-number/YKPSZ3JIMECAT2NNPXHSVPGJF7/graph.json","fetch_events":"https://pith.science/api/pith-number/YKPSZ3JIMECAT2NNPXHSVPGJF7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YKPSZ3JIMECAT2NNPXHSVPGJF7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YKPSZ3JIMECAT2NNPXHSVPGJF7/action/storage_attestation","attest_author":"https://pith.science/pith/YKPSZ3JIMECAT2NNPXHSVPGJF7/action/author_attestation","sign_citation":"https://pith.science/pith/YKPSZ3JIMECAT2NNPXHSVPGJF7/action/citation_signature","submit_replication":"https://pith.science/pith/YKPSZ3JIMECAT2NNPXHSVPGJF7/action/replication_record"}},"created_at":"2026-05-18T00:28:02.769975+00:00","updated_at":"2026-05-18T00:28:02.769975+00:00"}