A generic element of a ball $B$ over a set $C$ is an element $a\in B$ such that $a\not\in B'$ for any ball $B'$ definable over parameters in $C$ smaller than $B$.
Let $K$ be an ACVF and $a,b$ generics of $B_{\geq 0}(0)$ over $K$. If $b$ is a generic of $B_{>0}(a)$ over $K\cup\{a\}$, is it $a$ a generic of $B_{>0}(b)$ over $K\cup\{b\}$?
I see how to check the balls containing $b$ (since every element of a ball is its centre) but what about the balls that do not contain $b$? (If they don't use $b$ as a parameter then we have information since $b$ is a generic, however for the rest I don't know how to proceed)