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Culminating-point filter construction for particle points is distinguishedfrom torus construction for wave functions in the tangent objects of theirneighborhoods. Both constructions are not united by a general manifolddiffeomorphism, but are united by a map of a hidden conformal $S^{1}\timesS^{3}$ charge with harmonic (Maxwell) potentials into a physical space formedby culminating points, tangent objects, and Feynman connections. The particlesare obtained from three classes of eigensolutions of the homogeneous potentialequations on $S^{1}\times S^{3}$. The map of the $u(2)$ invariant vector fieldsinto the Dirac phase factors of the connections yields the electro-weakLagrangian with explicit mass operators for the massive leptons. The spectrumof massive particles is restricted by the small, manageable number ofeigensolution classes and an instability of the model for higher mass values.This instability also defines the huge numbers of filter elements needed forthe culminating points. Weinberg angle, current coupling constant, and leptonmasses are calculated or estimated from the renormalization of filterproperties. Consequences for particle astrophysics follow, on the one hand,from the restriction of particle classes and, on the other hand, from thesuggestion of new particles from the three classes e.g. of dark matter, of aconfinon for the hadrons, and of a prebaryon. Definitely excluded are e.g. SUSYconstructions, Higgs particles, and a quark gluon plasma: three-piece phenomafrom the confinons are always present.

Weinberg angle, current coupling constant, and mass of particles as properties of culminating-point filters - consequences for particle astrophysics