I don't think CLPW spreads from stems nor leaf fragments. CLPW is an annual plant. However CLPW does spread from its seeds in the seed head and the turions that develop in the axils of some of the leaves. The turions grow and develop as the plant matures. I think there is a point in time of growth or development where the turion becomes viable to produce a sprout of a new CLPW plant; similar to any plant that produces seeds. IMO not all newly developing seeds nor turions are active for new growth and it takes a stage of maturity for regrowth ability of a new plant. If the CLPW can be cut or removed before the turions are viable or mature or start to develop then non-turion parts of the plant will not re-sprout into a new plant. This assumes the seed head of the CLPW also has not fully developed.

A turion is a resistant plant bud that is found in certain aquatic plants, and can allow the plant to survive winter in the vegetative state (i.e., without setting seeds). The word “turio” is latin for a shoot or sprout (shoot in the sense of a plant stem and leaves), and is used in this case because a bud can develop into a shoot, as might happen with the turion in the late fall or spring after the ice has melted.