Maximum-gap derivative sampling conjecture for shift-invariant spaces

Let $V(\phi)$ be a shift-invariant space, let $k$ and $\nu$ be positive integers, and let $\\{x_i:i\in\mathbb{Z}\\}$ be a separated set. For a function $f$, consider the nonuniform samples of its derivatives $f^{(j)}(x_i)$ for $j=0,\dots,k-1$. Maximum-gap derivative sampling conjecture. If

$$\sup\limits_{i}(x_{i+\nu}-x_i)<k\nu,$$

then every function $f\in V(\phi)$ can be reconstructed stably from its nonuniform sample values $\\{f^{(j)}(x_i):j=0,\dots,k-1, i\in\mathbb{Z}\\}$. The statement generalizes the preceding maximum-gap sampling conjecture to simultaneous derivative sampling, but no resolution is given in the source.