  We present an effective unified theory based on noncommutative geometry for
the standard model with neutrino mixing, minimally coupled to gravity. The
unification is based on the symplectic unitary group in Hilbert space and on
the spectral action. It yields all the detailed structure of the standard model
with several predictions at unification scale. Besides the familiar predictions
for the gauge couplings as for GUT theories, it predicts the Higgs scattering
parameter and the sum of the squares of Yukawa couplings. From these relations
one can extract predictions at low energy, giving in particular a Higgs mass
around 170 GeV and a top mass compatible with present experimental value. The
geometric picture that emerges is that space-time is the product of an ordinary
spin manifold (for which the theory would deliver Einstein gravity) by a finite
noncommutative geometry F. The discrete space F is of KO-dimension 6 modulo 8
and of metric dimension 0, and accounts for all the intricacies of the standard
model with its spontaneous symmetry breaking Higgs sector.
