The analytic approximation conjecture for Kronecker webs

Fix $k\geq 0$. Let $U\subset\Bbb R^n$ be an open subset containing $0$, and let $\cal W$ be a Kronecker web on $U$. A $k$-jet records the derivatives through order $k$ at the specified point.

Analytic approximation conjecture. There is an open subset $U'\subset U$ containing $0$ and a real-analytic Kronecker web $\cal W'$ on $U'$ whose $k$-jet at $0$ agrees with the $k$-jet of $\cal W$.

The conjecture is used to motivate an amplification involving translation-invariant webs and is needed for the paper's classification program. No resolution is supplied in the source.