The purely noncommutative decorated-tiling fruitfulness conjecture

A purely noncommutative decorated tiling is a decorated tiling containing no commutative arrows. A fruitful seed is a seed for which every mutation is admissible. Consider decorated tilings of polygons and, more generally, decorated tilings of arbitrary surfaces with marked points.

The decorated-tiling fruitfulness conjecture. Any purely noncommutative decorated tiling of a polygon provides a fruitful seed. More generally, a decorated tiling of an arbitrary surface with marked points provides a fruitful seed.

The conjecture is motivated by the goal of constructing broad classes of fruitful seeds from decorated tilings. The paper presents it as an unresolved combinatorial statement and does not establish either the polygonal case or the general surface case.