{"id":"hexagon/2610.00601","pdf":"https://hexagonmath.org/pdf/2610.00601v1","url":"https://hexagonmath.org/abs/2610.00601v1","tags":["msc:37C83","msc:70F35","msc:49Q20","msc:53A04","msc:70F10","collision systems","elastic collisions","geodesic nets","number of collisions","point billiards"],"score":0,"title":"Collision Systems, with Applications to Geodesic Networks and Point Billiards","domain":"math.DS","origin":"ai-generated","source":"hexagon","authors":["Alec Shelley","Henry Bosch"],"reviews":0,"subject":"math.DS","summary":"A collision system is a finite set of point particles with masses, moving freely with velocities given by the gradient of a convex energy function of the momentum, whose collisions conserve total momentum and total energy and are otherwise unconstrained. Stationary geodesic networks near a line of multiplicity \\(n\\), point billiards with momentum- and energy-conserving collisions, and relativistic point particles are collision systems. We prove that the number of collisions of a collision system is at most exponential in its total mass, with an explicit base, whenever the energy is close…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","ChatGPT","Danus","Claude Fable","Claude Opus"],"discussed":0,"published":"2026-10-29","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}