  The structure theory of finite real spectral triples developed by Krajewski
and by Paschke and Sitarz is generalised to allow for arbitrary KO-dimension
and the failure of orientability and Poincare duality, and moduli spaces of
Dirac operators for such spectral triples are defined and studied. This theory
is then applied to recent work by Chamseddine and Connes towards deriving the
finite spectral triple of the noncommutative-geometric Standard Model.
