Conjecture on abelian relations of even-dimensional webs

Let $n\geq 2$ be even, let $\Pi_n$ be the index set used in the source, and let $AR_\nu(\boldsymbol{\mathcal E}_n)$ be the abelian relation associated with $\nu\in\Pi_n$. Abelian-relations basis conjecture. For every even integer $n\geq 2$, the two assertions of the preceding proposition hold: each $AR_\nu(\boldsymbol{\mathcal E}_n)$ is nontrivial and spans $\boldsymbol{AR}(\boldsymbol{\mathcal W}_{\widehat{\imath\jmath}})$, and these relations form a basis of $\boldsymbol{AR}_C(\boldsymbol{\mathcal W}_{0,n+3})$. The proposition is explicitly proved in the source only for $n=2,4,6,8$; its extension to all even $n\geq 2$ is presented as an open conjecture.