{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:2JSMTK2UBGUCQOZZ6SXAAUI2VX","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":"81be787a9274ceb5cf3430e8873335e974635f951029d3d3d8211adedbfa47b1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-24T11:44:45Z","title_canon_sha256":"e0ed3f60b86cd452f7fc7764da9e6a093cb6911a76d9480ecaa77c01a6d60be0"},"schema_version":"1.0","source":{"id":"1110.5203","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5203","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5203v3","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5203","created_at":"2026-05-18T03:54:49Z"},{"alias_kind":"pith_short_12","alias_value":"2JSMTK2UBGUC","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"2JSMTK2UBGUCQOZZ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"2JSMTK2U","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:02b1fd16d76c46502d0da7fb6399399cdb2f419e3210b4cef33932372819fdad","target":"graph","created_at":"2026-05-18T03:54:49Z","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":"Let $t$ be a rooted tree and $n_i(t)$ the number of nodes in $t$ having $i$ children. The degree sequence $(n_i(t),i\\geq 0)$ of $t$ satisfies $\\sum_{i\\ge 0} n_i(t)=1+\\sum_{i\\ge 0} in_i(t)=|t|$, where $|t|$ denotes the number of nodes in $t$. In this paper, we consider trees sampled uniformly among all trees having the same degree sequence $\\ds$; we write $`P_\\ds$ for the corresponding distribution. Let $\\ds(\\kappa)=(n_i(\\kappa),i\\geq 0)$ be a list of degree sequences indexed by $\\kappa$ corresponding to trees with size $\\nk\\to+\\infty$. We show that under some simple and natural hypotheses on $","authors_text":"Jean-Fran\\c{c}ois Marckert, Nicolas Broutin","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-24T11:44:45Z","title":"Asymptotics of trees with a prescribed degree sequence and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5203","kind":"arxiv","version":3},"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":"sha256:6936cf772d11e528b83a603b5c02f6973d900637c595ba07f157649b6591ac4c","target":"record","created_at":"2026-05-18T03:54:49Z","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":"81be787a9274ceb5cf3430e8873335e974635f951029d3d3d8211adedbfa47b1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-24T11:44:45Z","title_canon_sha256":"e0ed3f60b86cd452f7fc7764da9e6a093cb6911a76d9480ecaa77c01a6d60be0"},"schema_version":"1.0","source":{"id":"1110.5203","kind":"arxiv","version":3}},"canonical_sha256":"d264c9ab5409a8283b39f4ae00511aadd0a9c2d768f7a41ccdb83ebc04702c12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d264c9ab5409a8283b39f4ae00511aadd0a9c2d768f7a41ccdb83ebc04702c12","first_computed_at":"2026-05-18T03:54:49.268837Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:49.268837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qj4DpjOiMO8SHjvMvUBUuHcUzGGbHkHasb9t2AoR3lj3ehkKYF0dE44Zs1utHEC+uwFVt2ts+a0EAbuCiD6MAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:49.269601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5203","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6936cf772d11e528b83a603b5c02f6973d900637c595ba07f157649b6591ac4c","sha256:02b1fd16d76c46502d0da7fb6399399cdb2f419e3210b4cef33932372819fdad"],"state_sha256":"92d8d17cccdf1ef9b3ae788893bc23e2cc10bf7f49ac54c185abc97b483400f6"}