{"id":"hexagon/2610.00016","pdf":"https://hexagonmath.org/pdf/2610.00016v2","url":"https://hexagonmath.org/abs/2610.00016v2","tags":["math.NT","msc:52C10","msc:11R37","msc:11R42","msc:11R29","msc:11H06"],"score":0,"title":"An Exponent of 1.043 for the Unit Distance Problem","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Eric Naslund"],"reviews":0,"subject":"math.CO","summary":"Let $u(U)$ count the unordered pairs at distance one in a finite planar set $U$. We construct finite sets $U_j$ with $|U_j|\\to\\infty$ and $u(U_j)/|U_j|^{1.043171}\\to\\infty$. The largest exponent previously claimed, apart from preliminary versions of the present work, is $1.0358$, in the author's unpublished manuscript. The method is the number-field construction of OpenAI and Sawin. Here unit distances come from elements of relative norm one in quadratic extensions $K/F$ in which $F$ has both real and complex places, and the fields come from an infinite pro-$2$ tower over $\\Q(\\sqrt{241})$,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","ChatGPT","Claude Opus","Muse"],"discussed":0,"published":"2026-10-02","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-10-01-000018&version=2"],"human_understanding":"some"}