The Picard-group generation conjecture for motives

Let $k$ be a field and let $\mathcal{M}_\sim(k)$ be the category of motives over $k$ for an adequate equivalence relation $\sim$. Let $\operatorname{Pic}(\mathcal{M}_\sim(k))$ denote its Picard group of invertible motives, let $\mathbb{L}$ be the Lefschetz motive, and call an Artin motive of square $1$ an Artin motive $A$ satisfying $A^{\otimes 2}\simeq \mathbf{1}$. Picard-group generation conjecture. For any field $k$, $\operatorname{Pic}(\mathcal{M}_\sim(k))$ is generated by $\mathbb{L}$ and Artin motives of square $1$. This is presented as a strengthening of the odd-weight invertible-motive conjecture and concerns the structure of the group of invertible motives; no general resolution is given.