Global convergence conjecture for polyflow approximations of stable systems

Consider the system $\dot{x}=f(x)$, and suppose that $x=0$ is an asymptotically stable equilibrium. Let $\psi(x_0,t)$ denote its solution with initial condition $x_0$, and let $\pol{N}(x_0,t)$ denote the $N$th polyflow approximation. Global convergence conjecture. There exists a way of computing the polyflow coefficients from $f$, on some neighborhood $K$ of $0$, such that, for all $x_0\in K$, the polyflow approximations satisfy

$$\forall t\geq 0,\qquad \lim_{N\rightarrow\infty}\pol{N}(x_0,t)=\psi(x_0,t).$$

The conjecture proposes that an appropriate choice of the polyflow coefficients can extend convergence beyond the Taylor radius of convergence to the entire nonnegative time interval for trajectories starting near an asymptotically stable equilibrium. The supplied text does not indicate whether this has been proved or disproved.