{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:N3ZKLAIMIOOEBVMMU5XMP5VR4I","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":"2be72f4f775abc9e11e6ac1a62eb4fbc6ee736f683c33393f33213138093ae2b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-20T17:41:26Z","title_canon_sha256":"5f0f0d53a9a6ca404f0ccc25203373d2be28d9d220cb2f6833b8153d31853232"},"schema_version":"1.0","source":{"id":"2607.18201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18201","created_at":"2026-07-21T02:22:27Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18201v1","created_at":"2026-07-21T02:22:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18201","created_at":"2026-07-21T02:22:27Z"},{"alias_kind":"pith_short_12","alias_value":"N3ZKLAIMIOOE","created_at":"2026-07-21T02:22:27Z"},{"alias_kind":"pith_short_16","alias_value":"N3ZKLAIMIOOEBVMM","created_at":"2026-07-21T02:22:27Z"},{"alias_kind":"pith_short_8","alias_value":"N3ZKLAIM","created_at":"2026-07-21T02:22:27Z"}],"graph_snapshots":[{"event_id":"sha256:c08f4711bb09afa75e1905310079a1c25a11bd97690804c24f77a7abbd5afbba","target":"graph","created_at":"2026-07-21T02:22:27Z","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/2607.18201/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"G\\'abor Lugosi, Luc Devroye, Neeladri Maitra","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-20T17:41:26Z","title":"Finding Adam in noisy trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18201","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:f7badafed7f682d5e9a9e539fc983bcbaf422e4c73d936f0202f417bdc49b1be","target":"record","created_at":"2026-07-21T02:22:27Z","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":"2be72f4f775abc9e11e6ac1a62eb4fbc6ee736f683c33393f33213138093ae2b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-07-20T17:41:26Z","title_canon_sha256":"5f0f0d53a9a6ca404f0ccc25203373d2be28d9d220cb2f6833b8153d31853232"},"schema_version":"1.0","source":{"id":"2607.18201","kind":"arxiv","version":1}},"canonical_sha256":"6ef2a5810c439c40d58ca76ec7f6b1e207d40ec426d0392a5e2662feec9fdacb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ef2a5810c439c40d58ca76ec7f6b1e207d40ec426d0392a5e2662feec9fdacb","first_computed_at":"2026-07-21T02:22:27.238379Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T02:22:27.238379Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O2U0fbErG27BI65kOtUSPkDVdoGy6Z3DKraxAa/JuS/K3cfImP3Wmhwc6mc8ImvNQXtpC3wPBvBR7kbOlYd2Bw==","signature_status":"signed_v1","signed_at":"2026-07-21T02:22:27.239239Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7badafed7f682d5e9a9e539fc983bcbaf422e4c73d936f0202f417bdc49b1be","sha256:c08f4711bb09afa75e1905310079a1c25a11bd97690804c24f77a7abbd5afbba"],"state_sha256":"a050078c73ef7bdabeea7ba89115d264ba9de15230948067f66b712fc0dc85fc"}