Continuity in q of the Podleś sphere for the spectral propinquity

Determine whether the spectral metric spaces (metric spectral triples) on the Podleś sphere depend continuously on the deformation parameter q in (0,1] with respect to Latrémolière’s spectral propinquity.

Background

While quantum Gromov–Hausdorff continuity for the Podleś sphere is known, the stronger topology induced by Latrémolière’s spectral propinquity is more delicate.

The authors note that it is unknown whether the spectral metric triples for the Podleś sphere vary continuously with q when measured by the spectral propinquity.