So far only the first generation of leptons and quarks with correct parity properties have been modelled by Sundance Bilson-Thompson using preons constituted of braids of spacetime as the building blocks.
[4] This provided a possible explanation for why ordering of the subcomponents matters (giving rise to colour charge) whereas in the older Rishon Model, this feature must be treated as an ad hoc assumption.
The first generation of fermions with correct charge and parity properties have been modelled using preons constituted of braids of spacetime as the building blocks.
[2] Bilson-Thompson's original paper suggested that the higher-generation fermions could be represented by more complicated braidings, although explicit constructions of these structures were not given.
The model was expressly generalized for an infinite number of generations and for the weak force bosons, but not for photons or gluons, in a 2008 paper by Bilson-Thompson, Hackett, Kauffman and Smolin.