Braids may be represented by matrices. Triality gives us three ways to embed a $2 \times 2$ matrix in a $3 \times 3$ one! That is three copies of the massless Bilson-Thompson spectrum, one for each generation pair.
If each entry is a bioctonion, this would be a $24$ (complex) dimensional operator. As a root of unity, this dimension is the neutrino phase $\pi /12$.
6 years ago