“…In Section 9 we show that all growth rates below ξ are growth rates of sum closed classes. Thus our characterization of these growth rates in [55] reduces to a characterization of the possible sequences of sum indecomposable classes, though that effort is far from trivial. It is not a coincidence that ξ is the growth rate of a sum closed class whose sum indecomposable members have the enumeration 1, 1, 2, 3, 4 8 (where 4 8 denotes an infinite sequence of 4s), though it is perhaps a coincidence that the same growth rate is achieved by a sum closed class whose sum indecomposable members have the enumeration 1, 1, 2, 4, 3, 3, 2, 1.…”