{"paper":{"title":"Linear Spectral Statistics for Entrywise-Transformed Spiked Wigner Matrices under Shifted $L^4$ Profile Admissibility","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ji Oon Lee, Tsz-Kin Chan","submitted_at":"2026-08-07T23:43:41Z","abstract_excerpt":"We prove a derivative-free analytic linear spectral statistics theorem for entrywise-transformed rank-one spiked Wigner matrices with a general microscopic noise law. The transform is required to be centered, variance-normalized, and admissible under the small translations generated by the spike: its shifted mean and second moment have first- and second-order profiles, while its centered shifted fourth cumulants and fourth tails are stable. At every microscopic shift we construct an explicit uniformly bounded three-point variable matching the first four centered moments of the target entry exa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.07820","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/2608.07820/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"}