{"paper":{"title":"On the Diameter of Finite Sidon Sets","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Daniel Carter, Kevin O'Bryant, Zach Hunter","submitted_at":"2023-10-30T21:33:06Z","abstract_excerpt":"We prove that the diameter of a Sidon set (also known as a Babcock sequence, Golomb ruler, or $B_2$ set) with $k$ elements is at least $k^2-b k^{3/2}-O(k)$ where $b\\le 1.96365$, a comparatively large improvement on past results. Equivalently, a Sidon set with diameter $n$ has at most $n^{1/2}+0.98183n^{1/4}+O(1)$ elements. The proof is conceptually simple but very computationally intensive, and the proof uses substantial computer assistance. We also provide a proof of $b\\le 1.99058$ that can be verified by hand, which still improves on past results. Finally, we prove that $g$-thin Sidon sets ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.20032","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/2310.20032/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"}