Irremediably singular quantum branched covers

We prove that the Natsume-Olsen non-commutative spheres ${\mathbb{S}}_{\theta }^{2n-1}$ dualize for rational deformation parameters to provide examples of quantum branched covers over their respective centers’ maximal spectra, embeddable into locally trivial $C^{\ast }$ bundles precisely when said spheres are classical; this, despite the bundles in question being of finite type over dimensional strata. The proof of the noted rigidity phenomenon relies on the quantum analogue of the 3-sphere’s Heegaard splitting as a pushout of two solid tori.