{"paper":{"title":"Finding Adam in noisy trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"G\\'abor Lugosi, Luc Devroye, Neeladri Maitra","submitted_at":"2026-07-20T17:41:26Z","abstract_excerpt":"We consider the problem of finding the root vertex of a random uniform attachment tree, when the union of the unlabeled tree and an Erd\\H{o}s-R\\'enyi random graph $\\mathbb{G}(n,p)$ is observed. We prove that, as long as $p=o(\\log n /n)$, for any $\\varepsilon>0$, one can construct a confidence set of vertices of size $K(\\varepsilon)$ that depends only on $\\varepsilon$ and not on $n$, such that it contains the root with probability at least $1-\\varepsilon$. This affirms a conjecture of Crane and Xu (2021). Our approach ranks vertices by their Jordan centrality in the largest component of the sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18201","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/2607.18201/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"}