Uniform bounded elementary generation of Chevalley groups

In this paper we establish a definitive result which almost completely closes the problem of bounded elementary generation for Chevalley groups of rank $\ge 2$ over arbitrary Dedekind rings $R$ of arithmetic type, with uniform bounds. Namely, we show that for every reduced irreducible root system $\mathrm{\Phi }$ of rank $\ge 2$ there exists a universal bound $L=L(\mathrm{\Phi })$ such that the simply connected Chevalley groups $G(\mathrm{\Phi },R)$ have elementary width $\le L$ for all Dedekind rings of arithmetic type $R$.