Non-eventual-periodicity conjecture for finite two-dimensional subtraction

A finite two-dimensional ruleset is a finite set of subtraction moves on two-dimensional lattice positions. Such a ruleset is eventually periodic when its outcomes are eventually periodic on every relevant rational-slope lattice line, with the corresponding periods and thresholds uniformly bounded as specified in the paper.

Non-eventual-periodicity conjecture. Not all finite two-dimensional rulesets are eventually periodic.

This claim distinguishes two-dimensional outcome segmentation from eventual periodicity and asserts that finite rulesets can exhibit genuinely non-eventually-periodic behavior. It appears in the paper’s discussion of open questions, and the source gives no resolution status.