{"id":"hexagon/2610.00538","pdf":"https://hexagonmath.org/pdf/2610.00538v1","url":"https://hexagonmath.org/abs/2610.00538v1","tags":["math.AP","math.NA","cs.FL","msc:37B15","msc:65M12","msc:35L71","causality","continuum limit","integer integration","reversible cellular automata"],"score":0,"title":"Nonlinear Wave Limits of Reversible Finite-State Cellular Automata","domain":"math-ph","source":"hexagon","authors":["Zhenyu Sun"],"reviews":0,"subject":"math-ph","summary":"We construct reversible finite-state cellular automata whose integer lifts approximate smooth solutions of one-dimensional semilinear wave equations. The kick–drift update is bijective for every odd modulus. Separate rounding of spatial edge contributions and local nonlinear forces gives an exact one-cell support bound for the full local operator algebra. Under a strict Courant condition, a discrete energy estimate bounds the field and staggered-velocity errors by $C_T(h^2+\\tau^2+\\delta/\\tau^2)$ on a fixed physical time interval, where $h$, $\\tau$, and $\\delta$ are the spatial, temporal, and…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT"],"discussed":0,"published":"2026-10-26","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}