André's generalized Grothendieck period conjecture

Let $M$ be an André motive over a subfield $K\subset\mathbb{C}$ of finite transcendence degree over $\mathbb{Q}$. Let $c_M\in\Omega^{\mathrm{And}}_M(\mathbb{C})$ be the complex comparison point, and let $\overline{\{c_M\}}^{K-\mathrm{Zar}}$ denote its $K$-Zariski closure in the motivated period torsor $\Omega^{\mathrm{And}}_M$.

André's generalized Grothendieck period conjecture. One has

$$\dim_K\overline{\{c_M\}}^{K-\mathrm{Zar}}\geq \dim_K\Omega^{\mathrm{And}}_M-\operatorname{trdeg}_{\mathbb{Q}}K.$$

This generalizes the algebraic-number-field formulation by allowing finitely generated base fields; the paper states it as André's formulation, and it remains open in general.