Growth rates of permutation classes: from countable to uncountable

We establish that there is an algebraic number ξ ≈ 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.