Carbohydrate antigens belong to the thymus-independent (TI) class of antigens, and the key to this question is recognising the immunological consequences of that classification. Because these antigens engage B cells without recruiting CD4 T-helper cells, they cannot drive germinal-centre reactions. Without a germinal-centre response there is no class switching, no affinity maturation, and crucially no generation of long-lived memory B cells. This is exactly why a plain polysaccharide pneumococcal or meningococcal vaccine must be repeated and why conjugating the sugar to a protein carrier (converting it into a T-dependent antigen) is needed to create durable memory. So memory is the property these antigens do NOT possess. Reviewing the remaining choices confirms the rest are genuine TI features: the response is dominated by polyclonal IgM, the immunity itself is T-cell independent, and the antigens can be presented by repeating epitopes that crosslink B-cell receptors. The single option that does not belong, the false statement requested by the stem, is therefore Memory. \[\boxed{\text{Memory}}\]