{"paper":{"title":"On the Erdos Discrepancy Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Bart Selman, Carla P. Gomes, Ronan Le Bras","submitted_at":"2014-05-15T20:43:48Z","abstract_excerpt":"According to the Erd\\H{o}s discrepancy conjecture, for any infinite $\\pm 1$ sequence, there exists a homogeneous arithmetic progression of unbounded discrepancy. In other words, for any $\\pm 1$ sequence $(x_1,x_2,...)$ and a discrepancy $C$, there exist integers $m$ and $d$ such that $|\\sum_{i=1}^m x_{i \\cdot d}| > C$. This is an $80$-year-old open problem and recent development proved that this conjecture is true for discrepancies up to $2$. Paul Erd\\H{o}s also conjectured that this property of unbounded discrepancy even holds for the restricted case of completely multiplicative sequences (CM"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2510","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":""},"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"}