{"paper":{"title":"The Thickness of Infinite Sidon Sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Kevin O'Bryant","submitted_at":"2026-06-26T23:34:53Z","abstract_excerpt":"Let $\\gamma \\ge 1$. A set $A$ of nonnegative integers is a Sidon set if for each $d>0$ there is at most one pair $(a,b) \\in A \\times A$ with $d=a-b$. If there are at most $\\gamma$ pairs, then $A$ is a $\\gamma$-Golomb ruler. We prove that if $A$ is a $\\gamma$-Golomb ruler, then \\[\\liminf_{n\\to\\infty} \\frac{|A\\cap[0,n)|}{\\sqrt{n/\\log n}} \\le \\frac{2}{\\sqrt{\\log 2}} \\sqrt{\\gamma}.\\] There is a $\\gamma$-Golomb ruler $G$ with \\[ \\limsup_{n\\to\\infty} \\frac{|G\\cap[0,n)|}{\\sqrt n} \\ge \\frac{1}{\\sqrt2} \\sqrt{\\gamma}.\\]"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28651","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/2606.28651/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"}