Rational linearity conjecture for resonance components of formal CDGAs

Let $(A,d)$ be a connected, $q$-finite, and $q$-formal $\mathbb{k}$-CDGA. For $i\leq q$ and $s\geq 1$, let $\mathcal{R}^{i,s}(A)$ and $\mathcal{R}_{i,s}(A)$ denote the corresponding resonance varieties in $H^1(A)$. Rational linearity conjecture. In the setting of Theorem~, each irreducible component of $\mathcal{R}^{i,s}(A)$ and $\mathcal{R}_{i,s}(A)$ is a $\mathbb{k}$-linear subspace of $H^1(A)$ defined over $\mathbb{Q}$. This claim concerns the geometric structure of resonance for formal CDGAs; the supplied text does not state whether it has been proved or remains open.