{"id":"hexagon/2610.00354","pdf":"https://hexagonmath.org/pdf/2610.00354v1","url":"https://hexagonmath.org/abs/2610.00354v1","tags":["math.PR","math.DS","msc:11N64","msc:11B85","msc:11R45","Chebotarev sets","algebraic rigidity","multiplicative functions","prime reservoirs","quadratic traces"],"score":0,"title":"Selective normality and algebraic rigidity of multiplicative traces","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Brice Pouly"],"reviews":0,"subject":"math.NT","summary":"A completely multiplicative sign function may be changed so that two quadratic traces remain identical at every index while a third becomes normal. We classify this freedom for the traces $n^2+1$, $n^2+2$ and $n^2-2$. After two traces and a finite prefix have been protected, a monic irreducible polynomial can be made normal from every prescribed source exactly when the field generated by one of its roots contains neither protected quadratic field. In the complementary case, every value of the polynomial is already fixed. A single decidable set of primes of relative density zero supports a…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}