{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ODUD547NU4UTOPQIJIYEKFAMD6","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":"5a99c31a4f4ce132c0e2c4cc892157176cd37cdfddbb3baf59f2164422cb85fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-05T12:52:54Z","title_canon_sha256":"4280f9bb839393cafeb78a82228abf6d94f95349e8f9e3cf5df9101729c82e0f"},"schema_version":"1.0","source":{"id":"1511.01721","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01721","created_at":"2026-05-18T01:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01721v2","created_at":"2026-05-18T01:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01721","created_at":"2026-05-18T01:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"ODUD547NU4UT","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"ODUD547NU4UTOPQI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"ODUD547N","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:3d1a2f4a6095f603cf903bfaf0bf9fd126b3f637d1038b6dbbbb492783d1ec5d","target":"graph","created_at":"2026-05-18T01:03:50Z","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":"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 .","authors_text":"Hongsong Guo, Jean-Fran\\c{c}ois Delmas (CERMICS), Romain Abraham (MAPMO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-05T12:52:54Z","title":"Critical Multi-Type Galton-Watson Trees Conditioned to be Large"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01721","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":"sha256:780fad79cb58255c21e155532e3e393e29e73155ed37842199a0cd34588a1ace","target":"record","created_at":"2026-05-18T01:03:50Z","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":"5a99c31a4f4ce132c0e2c4cc892157176cd37cdfddbb3baf59f2164422cb85fa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-11-05T12:52:54Z","title_canon_sha256":"4280f9bb839393cafeb78a82228abf6d94f95349e8f9e3cf5df9101729c82e0f"},"schema_version":"1.0","source":{"id":"1511.01721","kind":"arxiv","version":2}},"canonical_sha256":"70e83ef3eda729373e084a3045140c1f978971072f3228f3a346dea40f999c24","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70e83ef3eda729373e084a3045140c1f978971072f3228f3a346dea40f999c24","first_computed_at":"2026-05-18T01:03:50.927344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:50.927344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Waz0ykPzpJfAC27IppwqGr5+J2T8lcZkgrldYgC6bYVfwCI9NPuNm3+CiBRWAU2stBiINmC1LXx8+yvYIm2EBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:50.927877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01721","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:780fad79cb58255c21e155532e3e393e29e73155ed37842199a0cd34588a1ace","sha256:3d1a2f4a6095f603cf903bfaf0bf9fd126b3f637d1038b6dbbbb492783d1ec5d"],"state_sha256":"88086337395baf496e26728f042c1172be1b5493ccfebb7ad80ce7a2c0411355"}