Nonsmooth classification with fixed Elliott invariant and comparison radius

We construct Borel families of simple unital approximately homogeneous C*-algebras and of minimal integer crossed products, each with one full Elliott invariant and radius of comparison one, for which isomorphism is exactly eventual equality E₀ of binary sequences. Each image is Borel and its isomorphism relation is Borel bireducible with E₀. The full invariant includes the entire trace simplex and its pairing with ordered K-theory. The families contain continuum many pairwise nonisomorphic algebras with the same first-order theory, answering Farah's 2014 question negatively. We also answer the crossed-product lifting question raised by Hirshberg and Phillips in 2019: an approximately homogeneous minimal crossed product of stable rank one admits an order-two automorphism of its full Elliott invariant which has no algebra-automorphism lift. The proof computes every projection-corner radius through a persistent Chern-class obstruction. The tower argument also shows that every minimal compact metrizable almost one-to-one extension of an infinite odometer has approximately homogeneous crossed product. GitHub repository