{"paper":{"title":"Matrix Discrepancy for Representations of Finite Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.GR","math.RT"],"primary_cat":"math.PR","authors_text":"Afonso S. Bandeira, Helmut B\\\"olcskei","submitted_at":"2026-06-10T15:06:06Z","abstract_excerpt":"Given a finite group $G$, we prove that there exist signs $\\varepsilon\\in\\{\\pm1\\}^G$ such that $$\\left\\| \\sum_{g\\in G} \\varepsilon_g\\rho(g) \\right\\|\\leq C\\, \\sqrt{|G|},$$ where $\\rho$ is the left regular representation of $G$, and $C$ is a universal constant. This special case of the Matrix Spencer conjecture was posed in [BKMZ24], where it was established for simple groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.12181","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/2606.12181/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"}