{"id":"67121194-71d4-4697-89a8-7946e7bfa09f","arxiv_id":"2504.12150","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":8.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For n >= 4, the paper establishes Sarnak's density hypothesis in the spectral aspect for GL_n(Z) cuspidal representations and uses it to prove the Diophantine exponent of the SL_n(Z[1/p])-action is optimal (kappa = 1).","lead":"This paper proves a density hypothesis for non-tempered cuspidal representations of GL_n(Z) in the spectral aspect, showing such exceptional representations are rare. The proof yields the optimal Diophantine exponent for the SL_n(Z[1/p]) action on a symmetric space, resolving a conjecture of Ghosh, Gorodnik, and Nevo.","discovery_kind":"extension","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-16T12:36:47.778882+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}