Representation stability for uniform-matroid holonomy primitives

For the uniform matroids $U_{2,n}$ of rank $2$, define the graded Lie algebra $cmathcal{L}(n)$ by

$$cmathrm{OS}(U_{2,n})^!=cmathcal{U}(cmathcal{L}(n)).$$

The sequence $cmathcal{L}(n)_i$ is representation stable when $n$ is sufficiently large.

Uniform-matroid onset conjecture. For fixed $i eggeq 3$, the sequence $cmathcal{L}(n)_i$ is representation stable past $n=2i-1$.

This gives a proposed sharp stability range for the holonomy Lie algebra associated with the Koszul dual of the Orlik–Solomon algebra. The statement is supported by computations, while no proof or resolution is supplied here.