{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7EI3D5H2UW4KYSV645Y2QDHDKP","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":"5f52c41ecef7a2b9cf12052d47999e06522b3677116365ee6f9ae95fd9bfdae1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-23T21:07:24Z","title_canon_sha256":"d7eb6eeaebc105c00145335f962b7a874c7c992f2670755ca2c202c9c57c3ffe"},"schema_version":"1.0","source":{"id":"1805.09425","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.09425","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"arxiv_version","alias_value":"1805.09425v4","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.09425","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"pith_short_12","alias_value":"7EI3D5H2UW4K","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"pith_short_16","alias_value":"7EI3D5H2UW4KYSV6","created_at":"2026-07-05T00:49:33Z"},{"alias_kind":"pith_short_8","alias_value":"7EI3D5H2","created_at":"2026-07-05T00:49:33Z"}],"graph_snapshots":[{"event_id":"sha256:1d5fecef4cb3631330c6db2f5e6ff551f89d668ad37a184bb865fa7517537ad6","target":"graph","created_at":"2026-07-05T00:49:33Z","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/1805.09425/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A recursive function on a tree is a function in which each leaf has a given value, and each internal node has a value equal to a function of the number of children, the values of the children, and possibly an explicitly specified random element $U$. The value of the root is the key quantity of interest in general. In this first study, all node values and function values are in a finite set $S$. In this note, we describe the limit behavior when the leaf values are drawn independently from a fixed distribution on $S$, and the tree $T_n$ is a random Galton--Watson tree of size $n$.","authors_text":"Luc Devroye, Nicolas Broutin, Nicolas Fraiman","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-23T21:07:24Z","title":"Recursive functions on conditional Galton--Watson trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.09425","kind":"arxiv","version":4},"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":"sha256:91eea9d934d9df09b39b04a608ae61f455ec0425217712c63625c3b15a755981","target":"record","created_at":"2026-07-05T00:49:33Z","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":"5f52c41ecef7a2b9cf12052d47999e06522b3677116365ee6f9ae95fd9bfdae1","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-05-23T21:07:24Z","title_canon_sha256":"d7eb6eeaebc105c00145335f962b7a874c7c992f2670755ca2c202c9c57c3ffe"},"schema_version":"1.0","source":{"id":"1805.09425","kind":"arxiv","version":4}},"canonical_sha256":"f911b1f4faa5b8ac4abee771a80ce353f095d3f3589f72385b50bdedbbc752da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f911b1f4faa5b8ac4abee771a80ce353f095d3f3589f72385b50bdedbbc752da","first_computed_at":"2026-07-05T00:49:33.873362Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:49:33.873362Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qv+snksyVrb/K+cRZm69UGbAWdVQAqjr3VtXVHLgpwO4BldimSOijV4tjA8k8A3S3k7WSbGtRem92WbvUI8oCA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:49:33.873756Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.09425","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91eea9d934d9df09b39b04a608ae61f455ec0425217712c63625c3b15a755981","sha256:1d5fecef4cb3631330c6db2f5e6ff551f89d668ad37a184bb865fa7517537ad6"],"state_sha256":"0b084b101b60d4c3eb5f2529bb751d8528bbcc0662aa1a1ca26e68dc058f3392"}