Mixed Tate motives over dual numbers conjecture

Let $F_{\varepsilon}=F[\varepsilon]/(\varepsilon^2)$, and let ${\cal Q}_{\bullet}(F_{\varepsilon})$ be the Lie coalgebra combining the non-Euclidean and Euclidean scissor-congruence coalgebras. A finite-dimensional graded comodule means a finite-dimensional object equipped with the compatible graded coaction of this Lie coalgebra. Mixed Tate motives over dual numbers conjecture. The category of finite-dimensional graded comodules over ${\cal Q}_{\bullet}(F_{\varepsilon})$ is naturally equivalent to a subcategory of the category of mixed Tate motives over $F_{\varepsilon}$. This proposes a motivic interpretation of the scissor-congruence coalgebra for dual numbers, relating its comodules to mixed Tate motives while asserting only an embedding into the full motivic category.