{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:RZWBLGPRFNNSPROFNT752EIMJA","short_pith_number":"pith:RZWBLGPR","schema_version":"1.0","canonical_sha256":"8e6c1599f12b5b27c5c56cffdd110c480a0f6ae130e631b685d9566daf982acb","source":{"kind":"arxiv","id":"2501.03195","version":1},"attestation_state":"computed","paper":{"title":"Parking on the Random Recursive Tree","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Alice Contat, Lucile Laulin","submitted_at":"2025-01-06T18:13:21Z","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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2501.03195","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-06T18:13:21Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"df13dad4e1102ef36c89a55028cd246117466f4d695be4693a6494fac32b1a78","abstract_canon_sha256":"1546875955f0b7d069f61caa340ab2ecd273a9282972f467aa7368d595f24a1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:57:32.877433Z","signature_b64":"6KsdDaF582tJmtjSqy7TXe5K/Z4jYVfFZSCaRa5Hlps0F147pP1qNbvm0dktGT+dZYoyLs+nKgeiKg5h8bqIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e6c1599f12b5b27c5c56cffdd110c480a0f6ae130e631b685d9566daf982acb","last_reissued_at":"2026-07-05T09:57:32.877002Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:57:32.877002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parking on the Random Recursive Tree","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Alice Contat, Lucile Laulin","submitted_at":"2025-01-06T18:13:21Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.03195","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/2501.03195/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.03195","created_at":"2026-07-05T09:57:32.877059+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.03195v1","created_at":"2026-07-05T09:57:32.877059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.03195","created_at":"2026-07-05T09:57:32.877059+00:00"},{"alias_kind":"pith_short_12","alias_value":"RZWBLGPRFNNS","created_at":"2026-07-05T09:57:32.877059+00:00"},{"alias_kind":"pith_short_16","alias_value":"RZWBLGPRFNNSPROF","created_at":"2026-07-05T09:57:32.877059+00:00"},{"alias_kind":"pith_short_8","alias_value":"RZWBLGPR","created_at":"2026-07-05T09:57:32.877059+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/RZWBLGPRFNNSPROFNT752EIMJA","json":"https://pith.science/pith/RZWBLGPRFNNSPROFNT752EIMJA.json","graph_json":"https://pith.science/api/pith-number/RZWBLGPRFNNSPROFNT752EIMJA/graph.json","events_json":"https://pith.science/api/pith-number/RZWBLGPRFNNSPROFNT752EIMJA/events.json","paper":"https://pith.science/paper/RZWBLGPR"},"agent_actions":{"view_html":"https://pith.science/pith/RZWBLGPRFNNSPROFNT752EIMJA","download_json":"https://pith.science/pith/RZWBLGPRFNNSPROFNT752EIMJA.json","view_paper":"https://pith.science/paper/RZWBLGPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.03195&json=true","fetch_graph":"https://pith.science/api/pith-number/RZWBLGPRFNNSPROFNT752EIMJA/graph.json","fetch_events":"https://pith.science/api/pith-number/RZWBLGPRFNNSPROFNT752EIMJA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RZWBLGPRFNNSPROFNT752EIMJA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RZWBLGPRFNNSPROFNT752EIMJA/action/storage_attestation","attest_author":"https://pith.science/pith/RZWBLGPRFNNSPROFNT752EIMJA/action/author_attestation","sign_citation":"https://pith.science/pith/RZWBLGPRFNNSPROFNT752EIMJA/action/citation_signature","submit_replication":"https://pith.science/pith/RZWBLGPRFNNSPROFNT752EIMJA/action/replication_record"}},"created_at":"2026-07-05T09:57:32.877059+00:00","updated_at":"2026-07-05T09:57:32.877059+00:00"}