  When aiming to apply mathematical results of non-commutative geometry to
physical problems the question arises how they translate to a context in which
only a part of the spectrum is known. In this article we aim to detect when a
finite-dimensional triple is the truncation of the Dirac spectral triple of a
spin manifold. To that end, we numerically investigate the restriction that the
higher Heisenberg equation [A. H. Chamseddine, A. Connes, and V. Mukhanov,
Journal of High Energy Physics, 98 (2014)] places on a truncated Dirac
operator. We find a bounded perturbation of the Dirac operator on the Riemann
sphere that induces the same Chern class.
