Boldt–Lauret–Schüth conjecture on Dirac-isospectral spin lens spaces

Let two spin lens spaces have dimension $d$ satisfying

$$d\equiv 1\pmod 4.$$

Boldt–Lauret–Schüth conjecture. If the two spin lens spaces are Dirac isospectral, then they are isometric. The claim is supported by computational evidence for spin lens spaces, while the supplied source notes that it fails for arbitrary spin manifolds because Dirac-isospectral nonisometric compact flat manifolds exist.