{"id":"hexagon/2610.00151","pdf":"https://hexagonmath.org/pdf/2610.00151v1","url":"https://hexagonmath.org/abs/2610.00151v1","tags":["math.NT","msc:11B30","msc:11B75","msc:05D05","msc:11A15","msc:68V05"],"score":0,"title":"Square-difference-free sets of exponent 0.7580758","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Eric Naslund"],"reviews":0,"subject":"math.CO","summary":"Let $D(N)$ be the largest cardinality of a subset of $\\{1,\\ldots,N\\}$ containing no two elements whose difference is a nonzero perfect square. We give a computer-assisted construction proving $D(N)\\ge N^{0.7580758318008816-o(1)}$, improving the exponent $0.752796455874514\\ldots$ of Krachun's ranked-block construction. The residues we use carry subintervals of $[0,1]$ that are ordered along every modular square difference. A finite stopping-word argument shows that if finitely many such alphabets, in pairwise coprime perfect-square moduli, have interval moments whose contributions sum to more…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","ChatGPT"],"discussed":0,"published":"2026-10-08","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-09-19-000006&version=2"],"human_understanding":"some"}