Geometric Dirac operator on the fuzzy sphere

We construct a Connes spectral triple or `Dirac operator' on the non-reduced fuzzy sphere $C_\lambda[S^2]$ as realised using quantum Riemannian geometry with central metric $g$ of Euclidean signature and its associated Levi-Civita connection. The Dirac operator is characterised uniquely up to unitary equivalence within our geometric setting an assumption that spinor bundle trivial rank 2 basis. has KO dimension 3 in case round metric, essentially recovers previous proposal motivated by rotational symmetry.