{"paper":{"title":"Hitting Arithmetic Progressions at the Square-Root Scale","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Samuel Korsky","submitted_at":"2026-06-01T07:02:08Z","abstract_excerpt":"For positive integers $N$ and $k$, let $f(N,k)$ be the minimum size of a set $A\\subseteq\\{0,1,\\ldots,N-1\\}$ which intersects every $k$-term arithmetic progression contained in $\\{0,1,\\ldots,N-1\\}$. Brown and Freedman introduced this hitting problem for arithmetic progressions and studied it for growing $k$. The square-root scale $k=\\sqrt N$ is a natural transition point. Truss proved \\[\n  f(n^2,n)>n+\\frac12 n^{1/2}-2. \\] We improve the leading constant in the second-order term, proving \\[\n  f(n^2,n)\\ge n+\\left(\\frac1{\\sqrt2}+o(1)\\right)n^{1/2}. \\] On the upper-bound side, Brown and Freedman pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01780","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/2606.01780/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"}