Conjectured differentiability and sequence-independence of fluid limits

Let $z$ be a fluid limit with initial condition $z(0)=x$, where $x=\lim_n x^n/|x^n|$, and let $V_i$ denote the neighborhood associated with coordinate $i$. The right derivative at $0$ is denoted by $z'(0)$. Differentiability and sequence-independence conjecture. All coordinates of every fluid limit $z$ have right derivatives at $0$, even when there exists $i$ such that $x_j=z_j(0)=0$ for all $j\in V_i$. Moreover, the right derivative $z'(0)$ depends only on $x$ and not on the sequence $x^n$. If this holds, then all fluid limits are deterministic functions. The conjecture concerns the behavior and uniqueness of fluid limits at the boundary of the state space; the supplied text gives no resolution.