{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:UPWXBX63PEVX3ARJI63DLPHULM","short_pith_number":"pith:UPWXBX63","canonical_record":{"source":{"id":"2211.02317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-04T08:41:01Z","cross_cats_sorted":[],"title_canon_sha256":"49487a347369e5e3218d8792b4a46ac7d4f9d895abb9e385a4f7c34408b497e7","abstract_canon_sha256":"61f081f1c5e80bc0cdd8a6a6f8e8b3884001a3d671fa71b4521691d97c8b1848"},"schema_version":"1.0"},"canonical_sha256":"a3ed70dfdb792b7d822947b635bcf45b3c065c016c38100af16a8e9415819ef7","source":{"kind":"arxiv","id":"2211.02317","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.02317","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"arxiv_version","alias_value":"2211.02317v1","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.02317","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"pith_short_12","alias_value":"UPWXBX63PEVX","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"pith_short_16","alias_value":"UPWXBX63PEVX3ARJ","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"pith_short_8","alias_value":"UPWXBX63","created_at":"2026-07-05T05:13:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:UPWXBX63PEVX3ARJI63DLPHULM","target":"record","payload":{"canonical_record":{"source":{"id":"2211.02317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-04T08:41:01Z","cross_cats_sorted":[],"title_canon_sha256":"49487a347369e5e3218d8792b4a46ac7d4f9d895abb9e385a4f7c34408b497e7","abstract_canon_sha256":"61f081f1c5e80bc0cdd8a6a6f8e8b3884001a3d671fa71b4521691d97c8b1848"},"schema_version":"1.0"},"canonical_sha256":"a3ed70dfdb792b7d822947b635bcf45b3c065c016c38100af16a8e9415819ef7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:13:14.056032Z","signature_b64":"tRHlHdIJOqSm6wdCYd3M/Sge10M5P1l0lN6p+nUsknIKfRs3eIf1aPqZUOa8xNnKkrYcCtaf78X3OtnuROwNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3ed70dfdb792b7d822947b635bcf45b3c065c016c38100af16a8e9415819ef7","last_reissued_at":"2026-07-05T05:13:14.055615Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:13:14.055615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.02317","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:13:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kVJv2ZxhAQw/IKBLIydnEIBZcS2Q+ZANv4Luhmg/GkRopolgXSjdxs4Xgj3l6+FLDMTm6TB9IOdNzo0nT9yuCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:44:05.421977Z"},"content_sha256":"1e4c5bfb192181427cc1221ef95047f3a7cb8fac5ea71517aea7d97dd228df5e","schema_version":"1.0","event_id":"sha256:1e4c5bfb192181427cc1221ef95047f3a7cb8fac5ea71517aea7d97dd228df5e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:UPWXBX63PEVX3ARJI63DLPHULM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditioning (sub)critical L{\\'e}vy trees by their maximal degree: Decomposition and local limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jean-Fran\\c{c}ois Delmas (CERMICS), Michel Nassif (MAP5 - UMR 8145), Romain Abraham (IDP)","submitted_at":"2022-11-04T08:41:01Z","abstract_excerpt":"We study the maximal degree of (sub)critical L{\\'e}vy trees which arise as the scaling limits of Bienaym{\\'e}-Galton-Watson trees. We determine the genealogical structure of large nodes and establish a Poissonian decomposition of the tree along those nodes. Furthermore, we make sense of the distribution of the L{\\'e}vy tree conditioned to have a fixed maximal degree. In the case where the L{\\'e}vy measure is diffuse, we show that the maximal degree is realized by a unique node whose height is exponentially distributed and we also prove that the conditioned L{\\'e}vy tree can be obtained by graf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02317","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.02317/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T05:13:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yoyKqA6NEorUAEiF4DjKAyYJtA12egaR+DdHn9yHlDL92M/CfUj+F+u1rHMVBAY/E7ceAAHAJyutrpMvdRCbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T03:44:05.422471Z"},"content_sha256":"a5ca9e88f10971fd53c5c26f2f6ee26554659132797170404a009ea99beb41d3","schema_version":"1.0","event_id":"sha256:a5ca9e88f10971fd53c5c26f2f6ee26554659132797170404a009ea99beb41d3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UPWXBX63PEVX3ARJI63DLPHULM/bundle.json","state_url":"https://pith.science/pith/UPWXBX63PEVX3ARJI63DLPHULM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UPWXBX63PEVX3ARJI63DLPHULM/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":"2026-08-11T03:44:05Z","links":{"resolver":"https://pith.science/pith/UPWXBX63PEVX3ARJI63DLPHULM","bundle":"https://pith.science/pith/UPWXBX63PEVX3ARJI63DLPHULM/bundle.json","state":"https://pith.science/pith/UPWXBX63PEVX3ARJI63DLPHULM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UPWXBX63PEVX3ARJI63DLPHULM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:UPWXBX63PEVX3ARJI63DLPHULM","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":"61f081f1c5e80bc0cdd8a6a6f8e8b3884001a3d671fa71b4521691d97c8b1848","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-04T08:41:01Z","title_canon_sha256":"49487a347369e5e3218d8792b4a46ac7d4f9d895abb9e385a4f7c34408b497e7"},"schema_version":"1.0","source":{"id":"2211.02317","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.02317","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"arxiv_version","alias_value":"2211.02317v1","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.02317","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"pith_short_12","alias_value":"UPWXBX63PEVX","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"pith_short_16","alias_value":"UPWXBX63PEVX3ARJ","created_at":"2026-07-05T05:13:14Z"},{"alias_kind":"pith_short_8","alias_value":"UPWXBX63","created_at":"2026-07-05T05:13:14Z"}],"graph_snapshots":[{"event_id":"sha256:a5ca9e88f10971fd53c5c26f2f6ee26554659132797170404a009ea99beb41d3","target":"graph","created_at":"2026-07-05T05:13:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2211.02317/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the maximal degree of (sub)critical L{\\'e}vy trees which arise as the scaling limits of Bienaym{\\'e}-Galton-Watson trees. We determine the genealogical structure of large nodes and establish a Poissonian decomposition of the tree along those nodes. Furthermore, we make sense of the distribution of the L{\\'e}vy tree conditioned to have a fixed maximal degree. In the case where the L{\\'e}vy measure is diffuse, we show that the maximal degree is realized by a unique node whose height is exponentially distributed and we also prove that the conditioned L{\\'e}vy tree can be obtained by graf","authors_text":"Jean-Fran\\c{c}ois Delmas (CERMICS), Michel Nassif (MAP5 - UMR 8145), Romain Abraham (IDP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-04T08:41:01Z","title":"Conditioning (sub)critical L{\\'e}vy trees by their maximal degree: Decomposition and local limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.02317","kind":"arxiv","version":1},"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":"sha256:1e4c5bfb192181427cc1221ef95047f3a7cb8fac5ea71517aea7d97dd228df5e","target":"record","created_at":"2026-07-05T05:13:14Z","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":"61f081f1c5e80bc0cdd8a6a6f8e8b3884001a3d671fa71b4521691d97c8b1848","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-04T08:41:01Z","title_canon_sha256":"49487a347369e5e3218d8792b4a46ac7d4f9d895abb9e385a4f7c34408b497e7"},"schema_version":"1.0","source":{"id":"2211.02317","kind":"arxiv","version":1}},"canonical_sha256":"a3ed70dfdb792b7d822947b635bcf45b3c065c016c38100af16a8e9415819ef7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a3ed70dfdb792b7d822947b635bcf45b3c065c016c38100af16a8e9415819ef7","first_computed_at":"2026-07-05T05:13:14.055615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:13:14.055615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tRHlHdIJOqSm6wdCYd3M/Sge10M5P1l0lN6p+nUsknIKfRs3eIf1aPqZUOa8xNnKkrYcCtaf78X3OtnuROwNAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:13:14.056032Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.02317","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e4c5bfb192181427cc1221ef95047f3a7cb8fac5ea71517aea7d97dd228df5e","sha256:a5ca9e88f10971fd53c5c26f2f6ee26554659132797170404a009ea99beb41d3"],"state_sha256":"80a01df9d3569a0745bfd895ebf43f124ff0c52df6fcb0630778918fb3d90fde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qV+s6w+Or4k3u3yaO2sjZKigVSo2nqBGbrilnYdti31Uo88LEUUXBV+LmSozQqbodKcRWuW1FUpboSUXjn89CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T03:44:05.428229Z","bundle_sha256":"acd0770d21c53d5f82885eb464ed2a977a86ba5a851527d986b772c06f0c195e"}}