{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:F2JV7TBAET6G3JGVOQ7S3MN4EM","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":"1950be6a6453b25a0bcb234afa786dadcb6217df64a49f9cf3402c18777cb9a6","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2005-11-21T12:52:15Z","title_canon_sha256":"8debeb1a82e995e47e15f0458957f00fddc2e91acd75b7cac06540d74290d444"},"schema_version":"1.0","source":{"id":"math/0511515","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0511515","created_at":"2026-07-04T14:51:43Z"},{"alias_kind":"arxiv_version","alias_value":"math/0511515v1","created_at":"2026-07-04T14:51:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0511515","created_at":"2026-07-04T14:51:43Z"},{"alias_kind":"pith_short_12","alias_value":"F2JV7TBAET6G","created_at":"2026-07-04T14:51:43Z"},{"alias_kind":"pith_short_16","alias_value":"F2JV7TBAET6G3JGV","created_at":"2026-07-04T14:51:43Z"},{"alias_kind":"pith_short_8","alias_value":"F2JV7TBA","created_at":"2026-07-04T14:51:43Z"}],"graph_snapshots":[{"event_id":"sha256:7cfdff264566f57262d5f274affcd1b038333fda09e5f9763cc8fd7fc8713d0c","target":"graph","created_at":"2026-07-04T14:51:43Z","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/math/0511515/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We discuss several connections between discrete and continuous random trees. In the discrete setting, we focus on Galton-Watson trees under various conditionings. In particular, we present a simple approach to Aldous' theorem giving the convergence in distribution of the contour process of conditioned Galton-Watson trees towards the normalized Brownian excursion. We also briefly discuss applications to combinatorial trees. In the continuous setting, we use the formalism of real trees, which yields an elegant formulation of the convergence of rescaled discrete trees towards continuous objects. ","authors_text":"Jean-Francois Le Gall","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2005-11-21T12:52:15Z","title":"Random trees and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0511515","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:a436ac2253f14babe173e045f5758fdd813df87b434f8070181da351a2e4e21f","target":"record","created_at":"2026-07-04T14:51:43Z","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":"1950be6a6453b25a0bcb234afa786dadcb6217df64a49f9cf3402c18777cb9a6","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2005-11-21T12:52:15Z","title_canon_sha256":"8debeb1a82e995e47e15f0458957f00fddc2e91acd75b7cac06540d74290d444"},"schema_version":"1.0","source":{"id":"math/0511515","kind":"arxiv","version":1}},"canonical_sha256":"2e935fcc2024fc6da4d5743f2db1bc2308648b96ef8bd9f122131ec30800c00d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e935fcc2024fc6da4d5743f2db1bc2308648b96ef8bd9f122131ec30800c00d","first_computed_at":"2026-07-04T14:51:43.557522Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:51:43.557522Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yWUgoAt9XT/whYLrc8oKcuD1UrmI1lFvncaX9g++n4BccaMzy4y+uGvbLCLPeXPhW9slYked3BTivIiTVmCjAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:51:43.557931Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0511515","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a436ac2253f14babe173e045f5758fdd813df87b434f8070181da351a2e4e21f","sha256:7cfdff264566f57262d5f274affcd1b038333fda09e5f9763cc8fd7fc8713d0c"],"state_sha256":"1557513d0cde3b29384704d94b76f30dff986fb14b4b2b8809d17474dcd88a43"}