{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RZWBLGPRFNNSPROFNT752EIMJA","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":"1546875955f0b7d069f61caa340ab2ecd273a9282972f467aa7368d595f24a1c","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-06T18:13:21Z","title_canon_sha256":"df13dad4e1102ef36c89a55028cd246117466f4d695be4693a6494fac32b1a78"},"schema_version":"1.0","source":{"id":"2501.03195","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.03195","created_at":"2026-07-05T09:57:32Z"},{"alias_kind":"arxiv_version","alias_value":"2501.03195v1","created_at":"2026-07-05T09:57:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03195","created_at":"2026-07-05T09:57:32Z"},{"alias_kind":"pith_short_12","alias_value":"RZWBLGPRFNNS","created_at":"2026-07-05T09:57:32Z"},{"alias_kind":"pith_short_16","alias_value":"RZWBLGPRFNNSPROF","created_at":"2026-07-05T09:57:32Z"},{"alias_kind":"pith_short_8","alias_value":"RZWBLGPR","created_at":"2026-07-05T09:57:32Z"}],"graph_snapshots":[{"event_id":"sha256:404e61c6d53785aba516b16a0cb4dc67bfc62300232705bd2f5d5c902603f95b","target":"graph","created_at":"2026-07-05T09:57:32Z","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/2501.03195/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the parking process on the random recursive tree. We first prove that although the random recursive tree has a non-degenerate Benjamini--Schramm limit, the phase transition for the parking process appears at density $0$. We then identify the critical window for appearance of a positive flux of cars with high probability. In the case of binary car arrivals, this happens at density $ \\log (n)^{-2+o(1)}$ where $n$ is the size of the tree. This is the first work that studies the parking process on trees with possibly large degree vertices.","authors_text":"Alice Contat, Lucile Laulin","cross_cats":["math.CO"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-06T18:13:21Z","title":"Parking on the Random Recursive Tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03195","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":"sha256:71601172c0435c01fd6f7b0db601b3a2b3318f05e66fc68637dad4115ee46abd","target":"record","created_at":"2026-07-05T09:57:32Z","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":"1546875955f0b7d069f61caa340ab2ecd273a9282972f467aa7368d595f24a1c","cross_cats_sorted":["math.CO"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-06T18:13:21Z","title_canon_sha256":"df13dad4e1102ef36c89a55028cd246117466f4d695be4693a6494fac32b1a78"},"schema_version":"1.0","source":{"id":"2501.03195","kind":"arxiv","version":1}},"canonical_sha256":"8e6c1599f12b5b27c5c56cffdd110c480a0f6ae130e631b685d9566daf982acb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e6c1599f12b5b27c5c56cffdd110c480a0f6ae130e631b685d9566daf982acb","first_computed_at":"2026-07-05T09:57:32.877002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:57:32.877002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6KsdDaF582tJmtjSqy7TXe5K/Z4jYVfFZSCaRa5Hlps0F147pP1qNbvm0dktGT+dZYoyLs+nKgeiKg5h8bqIDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:57:32.877433Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.03195","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71601172c0435c01fd6f7b0db601b3a2b3318f05e66fc68637dad4115ee46abd","sha256:404e61c6d53785aba516b16a0cb4dc67bfc62300232705bd2f5d5c902603f95b"],"state_sha256":"6f2a124fcde113cfe02440ed624e320d53718520278946778b3eccc1fa7d1c26"}