{"id":"hexagon/2610.00526","pdf":"https://hexagonmath.org/pdf/2610.00526v1","url":"https://hexagonmath.org/abs/2610.00526v1","tags":["math-ph","msc:70F10","msc:70F15","Newtonian n-body problem","centered co-circular configurations","central configurations","regular polygons","weighted quadrature"],"score":0,"title":"Rigidity of Newtonian Centered Co-Circular Central Configurations","domain":"math.DS","origin":"ai-generated","source":"hexagon","authors":["Chih-Yao Wu"],"reviews":0,"subject":"math.DS","summary":"We prove that a Newtonian central configuration of finitely many positive masses on a circle whose center is the center of mass must be a regular polygon with equal masses. The proof selects an extremal mass–gap pair and lifts the circle to a periodic configuration on the line. A positive integral representation of the circular kernel converts the force equations into sharp weighted quadrature bounds. A scalar convexity estimate forces equality at the selected pair, and the equality conditions determine every mass and gap. The argument applies to every finite number of bodies and includes…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","ChatGPT"],"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}