{"paper":{"title":"Focused Width in Adversarial Fake Detection: A Separation","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Gao Huang","submitted_at":"2026-07-06T17:55:41Z","abstract_excerpt":"We study the adversarial fake detection model introduced by Mendelson, Paouris and Vershynin. In this model, a genuine sample is $\\pmb{X}\\sim N(0,\\pmb{I}_n)$, while a fake sample is produced as $\\pmb{X}+r\\pmb{t}({\\pmb{X}})$, where the adversary first observes $\\pmb{X}$ and then chooses an admissible perturbation $\\pmb{t}({\\pmb{X}})$ from a prescribed set $\\mathscr{T}\\subset\\mathbb{R}^n$. The central quantity is the detectability radius $r(\\mathscr{T})$, which formalizes the transition scale at which fake samples become reliably distinguishable from genuine ones. Mendelson, Paouris and Vershyni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.05379","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/2607.05379/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"}