{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:2JSMTK2UBGUCQOZZ6SXAAUI2VX","short_pith_number":"pith:2JSMTK2U","canonical_record":{"source":{"id":"1110.5203","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-24T11:44:45Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e0ed3f60b86cd452f7fc7764da9e6a093cb6911a76d9480ecaa77c01a6d60be0","abstract_canon_sha256":"81be787a9274ceb5cf3430e8873335e974635f951029d3d3d8211adedbfa47b1"},"schema_version":"1.0"},"canonical_sha256":"d264c9ab5409a8283b39f4ae00511aadd0a9c2d768f7a41ccdb83ebc04702c12","source":{"kind":"arxiv","id":"1110.5203","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:2JSMTK2UBGUCQOZZ6SXAAUI2VX","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5203","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-24T11:44:45Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"e0ed3f60b86cd452f7fc7764da9e6a093cb6911a76d9480ecaa77c01a6d60be0","abstract_canon_sha256":"81be787a9274ceb5cf3430e8873335e974635f951029d3d3d8211adedbfa47b1"},"schema_version":"1.0"},"canonical_sha256":"d264c9ab5409a8283b39f4ae00511aadd0a9c2d768f7a41ccdb83ebc04702c12","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:54:49.269601Z","signature_b64":"qj4DpjOiMO8SHjvMvUBUuHcUzGGbHkHasb9t2AoR3lj3ehkKYF0dE44Zs1utHEC+uwFVt2ts+a0EAbuCiD6MAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d264c9ab5409a8283b39f4ae00511aadd0a9c2d768f7a41ccdb83ebc04702c12","last_reissued_at":"2026-05-18T03:54:49.268837Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:54:49.268837Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5203","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9H+9juZ+8abCsEuaGwS/s1bi2/iqSEftWHsLeqNylkbdVfTCEiajjPZY0YLR9kul+KPfK6Xi8uRX8yj5ClZgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T05:28:23.712984Z"},"content_sha256":"6936cf772d11e528b83a603b5c02f6973d900637c595ba07f157649b6591ac4c","schema_version":"1.0","event_id":"sha256:6936cf772d11e528b83a603b5c02f6973d900637c595ba07f157649b6591ac4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:2JSMTK2UBGUCQOZZ6SXAAUI2VX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotics of trees with a prescribed degree sequence and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Marckert, Nicolas Broutin","submitted_at":"2011-10-24T11:44:45Z","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 $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5203","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:54:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q3uu4tiSGw/Opol77dnnr4n7/wxcszVjXoN0JprWxi5N5Fp2XRwUVuDdZ0f6n/e/O+5H46yKwb/O8UElfkLsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T05:28:23.713743Z"},"content_sha256":"02b1fd16d76c46502d0da7fb6399399cdb2f419e3210b4cef33932372819fdad","schema_version":"1.0","event_id":"sha256:02b1fd16d76c46502d0da7fb6399399cdb2f419e3210b4cef33932372819fdad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JSMTK2UBGUCQOZZ6SXAAUI2VX/bundle.json","state_url":"https://pith.science/pith/2JSMTK2UBGUCQOZZ6SXAAUI2VX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JSMTK2UBGUCQOZZ6SXAAUI2VX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-23T05:28:23Z","links":{"resolver":"https://pith.science/pith/2JSMTK2UBGUCQOZZ6SXAAUI2VX","bundle":"https://pith.science/pith/2JSMTK2UBGUCQOZZ6SXAAUI2VX/bundle.json","state":"https://pith.science/pith/2JSMTK2UBGUCQOZZ6SXAAUI2VX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JSMTK2UBGUCQOZZ6SXAAUI2VX/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jjSlEIzr2IVQ1a0b5gQU4EwbRWmE0CgSwyx/zNOgEg+XSuW/GgJNppgGsEPGpghUzYPnldk6l0n6DdFus9QwAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T05:28:23.719975Z","bundle_sha256":"4bdd2d8ae0d4fdb7069cea8b3945abe583e1b091082953b2cc8aba0c429353fc"}}