Burau's non-linearizability conjecture for even-dimensional webs

Let $n\geq 2$ be even, and let $\boldsymbol{\mathcal W}_{0,n+3}$ be the web by rational curves induced by the forgetful maps on $\mathcal M_{0,n+3}$. Burau's conjecture. The web $\boldsymbol{\mathcal W}_{0,n+3}$ is not linearizable. The conjecture concerns the apparent parity dichotomy in the properties of these webs; the source gives no resolution beyond the results discussed there.