We establish that there is an algebraic number $ξ\approx 2.30522$ such that while there are uncountably many growth rates of permutation classes arbitrarily close to $ξ,$ there are only countably many less than $ξ$. Central to the proof are various structural notions regarding generalized grid classes and a new property of permutation classes called concentration. The classification of growth rates up to $ξ$ is completed in a subsequent paper.