Fullness conjecture for logarithmic and logarithmic transfer-invariant motives

Let $\omega_{\operatorname{\mathbf{CI}}}^{\log}$ and $\omega_{\operatorname{\mathbf{CI}}}^{\rm ltr}$ be the functors from logarithmic and logarithmic transfer-invariant motives to their underlying ordinary Nisnevich sheaf categories, respectively. Fullness conjecture. The functors

$$\omega_{\operatorname{\mathbf{CI}}}^{\log}\quad\text{and}\quad\omega_{\operatorname{\mathbf{CI}}}^{\rm ltr}$$

are full. The preceding result establishes that these functors are faithful, exact, and conservative; the conjecture asks for the stronger fullness property and is presented as an expected result that the authors hope to prove soon.