Semi-primality conjecture for relative Chow motives

Let $X$ be a scheme, and let $F$ be the coefficient field. Let $\operatorname{CHM}(X)_F$ denote the category of Chow motives over $X$.

Semi-primality conjecture for relative Chow motives. The category $\operatorname{CHM}(X)_F$ is semi-primary.

This is the other conjecture identified in the supplied context and is intended to guide the construction and use of motivic weight structures with semi-primary hearts. The supplied text gives no evidence of a resolution, while the paper's results are described as unconditional.