Hi Yuri,
That is an interesting guess that would fit into my essay's framework because:
1) bosons and fermions are reciprocal lattices such that one is very large and the other is very small, and
2) the ratio of these two values is Dirac's Large Number 10^16 g/ 10^-24 g ~ 10^40 which is my anticipated "complexergy" number for our "Classical" Scale.
In my opinion, any TOE must have both boson and fermion basis "vectors/charges" in order to properly satisfy frame conditions such as the Coleman-Mandula Theorem. This also implies that Supersymmetry may be necessary.
I have been thinking about your ideas and Vladimir Tamari's ideas. He uses tetrahedra with spinning vertices. The tetrahedra are 3-dimensional and based on an SU(4) Lie Algebra. The vertex "spin" may be represented by a 1-dimensional U(1) Lie Algebra. Put it all together, and we have this 3:1 dimensional fundamental ratio that you so correctly emphasize. Look at the Lucas number series: 2,1,3,4,7,11,... and we recognize that 1 and 3 are sequential entries in this series.
Nonetheless, 3:1 is only part of the picture. I think we have something like a 28-D SU(29) TOE that decomposes into a (10+3+1)-D SU(11)xSU(4)xU(1) (times its Scaled and Supersymmetric 14-D reciprocal lattice) at lower energies, the SU(4)xU(1) represents Space and Time (its reciprocal lattice represents momentum and energy), and the 10-D SU(11) represents Scales that we can't see either because they are smaller than the Planck constant (Hyperspace), or larger than the speed-of-light constant (Multiverse).
Have Fun!
Dr. Cosmic Ray