Kontsevich–Soibelman lambda-conjecture for motivic vanishing cycles

Let $\underline{\operatorname{K}}_0(\operatorname{Sch}^{ft})$ and $\underline{\operatorname{K}}^{\hat{\mu}}(\operatorname{Sch}^{ft})$ be the motivic ring theories over $\mathbb{A}^1$, and let $\phi^{mot}$ be the morphism between them. $\lambda$-conjecture. The morphism

$$\phi^{mot}:\underline{\operatorname{K}}_0(\operatorname{Sch}^{ft})\to\underline{\operatorname{K}}^{\hat{\mu}}(\operatorname{Sch}^{ft})$$

of motivic ring theories over $\mathbb{A}^1$ is a morphism of $\lambda$-ring theories; equivalently, it commutes with the operations $\sigma^n$ of the $\lambda$-ring theories. If true, this would remove the stated compatibility problems in the definition of the motivic Donaldson–Thomas function and imply the integrality conjecture in the framework discussed by the authors.