Cellularity conjecture for $K(1)$-local motives over $\overline{\mathbb Q}$

The category of $K(1)$-local motives relative to $\overline{\mathbb Q}$ is the category under consideration, with cellular objects understood as those in the localizing subcategory generated by the unit. Cellularity conjecture. The category of $K(1)$-local motives relative to $\overline{\mathbb Q}$ is cellular. The conjecture reflects the expectation that, over an arithmetic point such as $\overline{\mathbb Q}$, the geometric and arithmetic obstructions to cellularity disappear. The source notes that a weaker formulation, restricted to dualizable $K(1)$-local motives, may be more reasonable; no resolution is given.