  Culminating-point filter construction for particle points is distinguished
from torus construction for wave functions in the tangent objects of their
neighborhoods. Both constructions are not united by a general manifold
diffeomorphism, but are united by a map of a hidden conformal $S^{1}\times
S^{3}$ charge with harmonic (Maxwell) potentials into a physical space formed
by culminating points, tangent objects, and Feynman connections. The particles
are obtained from three classes of eigensolutions of the homogeneous potential
equations on $S^{1}\times S^{3}$. The map of the $u(2)$ invariant vector fields
into the Dirac phase factors of the connections yields the electro-weak
Lagrangian with explicit mass operators for the massive leptons. The spectrum
of massive particles is restricted by the small, manageable number of
eigensolution classes and an instability of the model for higher mass values.
This instability also defines the huge numbers of filter elements needed for
the culminating points. Weinberg angle, current coupling constant, and lepton
masses are calculated or estimated from the renormalization of filter
properties. Consequences for particle astrophysics follow, on the one hand,
from the restriction of particle classes and, on the other hand, from the
suggestion of new particles from the three classes e.g. of dark matter, of a
confinon for the hadrons, and of a prebaryon. Definitely excluded are e.g. SUSY
constructions, Higgs particles, and a quark gluon plasma: three-piece phenoma
from the confinons are always present.
