The potentially interesting stuff happens at the top of p.13, where it is postulated that ''We will associate these three propagators with the three generations of elementary fermions''.

No reason is given, no discussion. It is simply an arbitrary setting, based on the superficial coincidence that two mathematical structures both involve the number 3.

All calculations on pp.4-12 happen in a Hilbert space of dimension 2 and a derived Hilbert space of dimension 3. But three generations of elementary fermions live in a tensor product of the Hilbert spaces of three elementary fermions, which consists of wave functions $\psi_{s_1s_2s_3}(x_1,x_2,x_3)$ with three spinor indices. Even if one could ignore the three position arguments (which is difficult to justify) this would require an 8-dimensional space of three spins.

The orthogonal projectors constructed in Section 5 are those of the 3-dimensional Hilbert space of traceless operators. There is no second 3-dimensional Hilbert space around, although p.13 claims there is.

Then it is said: ''This is just three times the number of states in the usual spin-1/2. We associate the tripling with the three generations.'' But what would have been needed for three generations is the number of states in the usual spin-1/2 to the third power.

Thus nothing at all has been demonstrated, except a misunderstanding of what it means to have 3 generations of elementary leptons.