Ulam stability of recursive subhomogeneous algebras

We prove that the class of all recursive subhomogeneous C*-algebras is Ulam stable with respect to von Neumann algebras. Thus an approximately additive, complex homogeneous, multiplicative and adjoint-preserving map on the whole unit ball is uniformly close to a genuine *-homomorphism, with one control function independent of the number of recursive pullbacks, matrix sizes, base spaces and target algebra. This answers a question of Alekseev, Farah and Thom from 2026. The result includes arbitrary compact Hausdorff base spaces and the nonunital version built from locally compact matrix-valued function algebras. The proof constructs one abelian subalgebra supporting every ideal of the recursive filtration. Correcting this subalgebra gives simultaneous control of all central sign combinations; the corrections on the homogeneous layers then have orthogonal ranges, so their errors combine by a maximum. GitHub repository: https://github.com/eulogica/ulam-stability-recursive-subhomogeneous Funding: This work is supported by ERC grant “Definable Algebraic Topology” (DAT, grant agreement No. 101077154; project DOI https://doi.org/10.3030/101077154). Funded by the European Union. Views and opinions expressed are however those of the author only and do not necessarily reflect those of the European Union or the European Research Council Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. The author was also partially supported by the Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GNSAGA) of the Istituto Nazionale di Alta Matematica (INdAM), and the University of Bologna.