Determining the number of Fermions and the number of Boson separately in an extended standard model

The minimum and maximum expectation number of elementary particles has been determined in various calculations and was found to be 61 and 68, respectively. Adding the hypothetical graviton this means 62 and 69 particles. However, in all these calculations, the used mathematics could not differentiate between Fermions and Bosons and any distinction was made a posteriori using phenomenological arguments. By contrast, the present work adds some refinement to the previous analysis so that the distinction between Fermions and Bosons is made a priori and calculated separately. Adding both numbers together we should naturally retrieve our earlier results.