{"paper":{"title":"On the Distribution of Rational Squares","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Michael Weiss","submitted_at":"2015-10-26T04:27:14Z","abstract_excerpt":"Let $a$ be a positive integer, and let $\\sigma(a)$ denote the least natural number $s$ such that an integer square lies between $s^2 a$ and $s^2 (a+1)$; let $\\tau_s(a)$ denote the number of such integer squares. The function $\\sigma(a)$ and the sequence $(\\tau_s(a))_{s \\in \\mathbb{Z}^+}$ are studied, and are observed to exhibit surprisingly chaotic behavior. Upper- and lower-bounds for $\\sigma(a)$ are derived, as are criteria for when they are sharp."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07362","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"}