{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:2EAPOZV2GEO5GLKHUXUBXRUDVJ","short_pith_number":"pith:2EAPOZV2","schema_version":"1.0","canonical_sha256":"d100f766ba311dd32d47a5e81bc683aa78bb825fc720291e5aca3ab3f1c73190","source":{"kind":"arxiv","id":"2607.02916","version":1},"attestation_state":"computed","paper":{"title":"Infinite collisions of simple random walks on random recursive trees generated by Bernoulli sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng Wang, Jia-shan Tang, Xian-Yuan Wu","submitted_at":"2026-07-03T03:23:17Z","abstract_excerpt":"In this paper, we study random recursive trees generated by Bernoulli sequences. Starting from a graph with two vertices and one edge, each new vertex is connected to the last vertex with probability $ p $, or to the second-last vertex with probability $ q = 1-p $, this recursive construction yields a random infinite recursive tree $T$. We prove that $T$ almost surely has exactly one topological end. Furthermore, we establish that $T$ has the infinite collision property: two independent simple random walks on $T$ collide infinitely often almost surely."},"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":"2607.02916","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-03T03:23:17Z","cross_cats_sorted":[],"title_canon_sha256":"edfba1ea10ce6a928703b41369612e051b1d8e0edd82afee2163a7f07ffb2150","abstract_canon_sha256":"ed4d0bb5572dfda848165d2532265bfe9ab943b93e993cdacee4f6b2014e0498"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-07T01:16:36.379786Z","signature_b64":"0e8OxnQ25xQdjR4EVmgG1uF3zGxLtc6GYpiXG88rKazLVj8rt7pZ1Nyfmuj0GIv5Z2b01pYFKSzNR++DHla2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d100f766ba311dd32d47a5e81bc683aa78bb825fc720291e5aca3ab3f1c73190","last_reissued_at":"2026-07-07T01:16:36.379379Z","signature_status":"signed_v1","first_computed_at":"2026-07-07T01:16:36.379379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinite collisions of simple random walks on random recursive trees generated by Bernoulli sequences","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng Wang, Jia-shan Tang, Xian-Yuan Wu","submitted_at":"2026-07-03T03:23:17Z","abstract_excerpt":"In this paper, we study random recursive trees generated by Bernoulli sequences. Starting from a graph with two vertices and one edge, each new vertex is connected to the last vertex with probability $ p $, or to the second-last vertex with probability $ q = 1-p $, this recursive construction yields a random infinite recursive tree $T$. We prove that $T$ almost surely has exactly one topological end. Furthermore, we establish that $T$ has the infinite collision property: two independent simple random walks on $T$ collide infinitely often almost surely."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02916","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/2607.02916/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":"2607.02916","created_at":"2026-07-07T01:16:36.379433+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.02916v1","created_at":"2026-07-07T01:16:36.379433+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02916","created_at":"2026-07-07T01:16:36.379433+00:00"},{"alias_kind":"pith_short_12","alias_value":"2EAPOZV2GEO5","created_at":"2026-07-07T01:16:36.379433+00:00"},{"alias_kind":"pith_short_16","alias_value":"2EAPOZV2GEO5GLKH","created_at":"2026-07-07T01:16:36.379433+00:00"},{"alias_kind":"pith_short_8","alias_value":"2EAPOZV2","created_at":"2026-07-07T01:16:36.379433+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/2EAPOZV2GEO5GLKHUXUBXRUDVJ","json":"https://pith.science/pith/2EAPOZV2GEO5GLKHUXUBXRUDVJ.json","graph_json":"https://pith.science/api/pith-number/2EAPOZV2GEO5GLKHUXUBXRUDVJ/graph.json","events_json":"https://pith.science/api/pith-number/2EAPOZV2GEO5GLKHUXUBXRUDVJ/events.json","paper":"https://pith.science/paper/2EAPOZV2"},"agent_actions":{"view_html":"https://pith.science/pith/2EAPOZV2GEO5GLKHUXUBXRUDVJ","download_json":"https://pith.science/pith/2EAPOZV2GEO5GLKHUXUBXRUDVJ.json","view_paper":"https://pith.science/paper/2EAPOZV2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.02916&json=true","fetch_graph":"https://pith.science/api/pith-number/2EAPOZV2GEO5GLKHUXUBXRUDVJ/graph.json","fetch_events":"https://pith.science/api/pith-number/2EAPOZV2GEO5GLKHUXUBXRUDVJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2EAPOZV2GEO5GLKHUXUBXRUDVJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2EAPOZV2GEO5GLKHUXUBXRUDVJ/action/storage_attestation","attest_author":"https://pith.science/pith/2EAPOZV2GEO5GLKHUXUBXRUDVJ/action/author_attestation","sign_citation":"https://pith.science/pith/2EAPOZV2GEO5GLKHUXUBXRUDVJ/action/citation_signature","submit_replication":"https://pith.science/pith/2EAPOZV2GEO5GLKHUXUBXRUDVJ/action/replication_record"}},"created_at":"2026-07-07T01:16:36.379433+00:00","updated_at":"2026-07-07T01:16:36.379433+00:00"}