The extension conjecture for Kronecker jet-webs

Let $\cal W$ be a Kronecker $k$-jet-web near $0\in\Bbb C^n$. A $k$-jet-web specifies the jet through order $k$ of a Kronecker web at the origin.

Extension conjecture. There are an open neighborhood $U\subset\Bbb C^n$ of $0$ and a Kronecker web $\cal W'$ on $U$ whose $k$-jet at $0$ agrees with $\cal W$.

This conjecture concerns whether formal or finite-order local web data can be realized by an actual Kronecker web. The source does not provide a general proof or resolution.