Automatic Jiang–Su absorption for amenable actions

Let G be a countable discrete group and let A be a nonzero simple separable unital nuclear C*-algebra that absorbs the Jiang–Su algebra Z. We prove that every action α: G ↷ A amenable in the sense of Anantharaman–Delaroche is cocycle conjugate to α ⊗ idZ. This answers the unital case of Szabó’s 2023 question on automatic Jiang–Su absorption for amenable actions. The theorem requires neither the UCT nor restrictions on the action on traces. The finite case is proved by constructing equivariant uniform property Gamma from central amenability coefficients. Two neighboring Hermite degrees produce almost circular Gaussian fields whose operator-valued quadratic forms have uniformly positive variance, even when the coefficients do not commute. Complemented partitions of unity then supply the tracial local-to-global argument. The purely infinite case follows from established absorption results. GitHub repository: https://github.com/eulogica/automatic-jiang-su-absorption