{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:ODUD547NU4UTOPQIJIYEKFAMD6","short_pith_number":"pith:ODUD547N","schema_version":"1.0","canonical_sha256":"70e83ef3eda729373e084a3045140c1f978971072f3228f3a346dea40f999c24","source":{"kind":"arxiv","id":"1511.01721","version":2},"attestation_state":"computed","paper":{"title":"Critical Multi-Type Galton-Watson Trees Conditioned to be Large","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hongsong Guo, Jean-Fran\\c{c}ois Delmas (CERMICS), Romain Abraham (MAPMO)","submitted_at":"2015-11-05T12:52:54Z","abstract_excerpt":"Under minimal condition, we prove the local convergence of a critical multi-type Galton-Watson tree conditioned on having a large total progeny by types towards a multi-type Kesten's tree. We obtain the result by generalizing Neveu's strong ratio limit theorem for aperiodic random walks on Z^d ."},"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":"1511.01721","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-05T12:52:54Z","cross_cats_sorted":[],"title_canon_sha256":"4280f9bb839393cafeb78a82228abf6d94f95349e8f9e3cf5df9101729c82e0f","abstract_canon_sha256":"5a99c31a4f4ce132c0e2c4cc892157176cd37cdfddbb3baf59f2164422cb85fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:50.927877Z","signature_b64":"Waz0ykPzpJfAC27IppwqGr5+J2T8lcZkgrldYgC6bYVfwCI9NPuNm3+CiBRWAU2stBiINmC1LXx8+yvYIm2EBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70e83ef3eda729373e084a3045140c1f978971072f3228f3a346dea40f999c24","last_reissued_at":"2026-05-18T01:03:50.927344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:50.927344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical Multi-Type Galton-Watson Trees Conditioned to be Large","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hongsong Guo, Jean-Fran\\c{c}ois Delmas (CERMICS), Romain Abraham (MAPMO)","submitted_at":"2015-11-05T12:52:54Z","abstract_excerpt":"Under minimal condition, we prove the local convergence of a critical multi-type Galton-Watson tree conditioned on having a large total progeny by types towards a multi-type Kesten's tree. We obtain the result by generalizing Neveu's strong ratio limit theorem for aperiodic random walks on Z^d ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01721","kind":"arxiv","version":2},"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":"1511.01721","created_at":"2026-05-18T01:03:50.927429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1511.01721v2","created_at":"2026-05-18T01:03:50.927429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01721","created_at":"2026-05-18T01:03:50.927429+00:00"},{"alias_kind":"pith_short_12","alias_value":"ODUD547NU4UT","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"ODUD547NU4UTOPQI","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"ODUD547N","created_at":"2026-05-18T12:29:34.919912+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/ODUD547NU4UTOPQIJIYEKFAMD6","json":"https://pith.science/pith/ODUD547NU4UTOPQIJIYEKFAMD6.json","graph_json":"https://pith.science/api/pith-number/ODUD547NU4UTOPQIJIYEKFAMD6/graph.json","events_json":"https://pith.science/api/pith-number/ODUD547NU4UTOPQIJIYEKFAMD6/events.json","paper":"https://pith.science/paper/ODUD547N"},"agent_actions":{"view_html":"https://pith.science/pith/ODUD547NU4UTOPQIJIYEKFAMD6","download_json":"https://pith.science/pith/ODUD547NU4UTOPQIJIYEKFAMD6.json","view_paper":"https://pith.science/paper/ODUD547N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1511.01721&json=true","fetch_graph":"https://pith.science/api/pith-number/ODUD547NU4UTOPQIJIYEKFAMD6/graph.json","fetch_events":"https://pith.science/api/pith-number/ODUD547NU4UTOPQIJIYEKFAMD6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ODUD547NU4UTOPQIJIYEKFAMD6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ODUD547NU4UTOPQIJIYEKFAMD6/action/storage_attestation","attest_author":"https://pith.science/pith/ODUD547NU4UTOPQIJIYEKFAMD6/action/author_attestation","sign_citation":"https://pith.science/pith/ODUD547NU4UTOPQIJIYEKFAMD6/action/citation_signature","submit_replication":"https://pith.science/pith/ODUD547NU4UTOPQIJIYEKFAMD6/action/replication_record"}},"created_at":"2026-05-18T01:03:50.927429+00:00","updated_at":"2026-05-18T01:03:50.927429+00:00"}