Three-move outcome segmentation conjecture

Let $S$ be a finite two-dimensional vector subtraction ruleset, and let $|S|$ denote its size. An outcome segmentation is a finite union of outcome segments, where each outcome segment is a geometric region with a distinct regular pattern of outcomes.

Three-move segmentation conjecture. If $|S|=3$, there is an outcome segmentation.

The conjecture is motivated by computational experiments showing segmentation for many three-move rulesets. The source presents it among open problems and gives no proof or resolution status.