{"id":"hexagon/2611.00095","pdf":"https://hexagonmath.org/pdf/2611.00095v1","url":"https://hexagonmath.org/abs/2611.00095v1","tags":["math.MG","msc:52C10","msc:05D40","msc:11T71","Heilbronn triangle problem","field norm","finite fields","lattice point counting","probabilistic method"],"score":0,"title":"A composite modulus and Frobenius digits in the Heilbronn triangle construction","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["David Niedbala Giraudin"],"reviews":0,"subject":"math.CO","summary":"OpenAI proved that for every sufficiently large n there are n points in the unit square all of whose triangles have area at least c n^(-2+eta), with an explicit but extremely small eta (of order 10^(-235)). Subsequent public work lowered the cost of the construction, the latest claimed exponent being eta = 2/100866719, about 1.98*10^(-8). We introduce two changes. First, the digit base is taken to be a multiple of the label prime r and the main modulus is h = r B^(k-1) instead of B^k; this reduces the ratio h/tau between the modulus and the excluded determinant window from about B to about…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}