Since we have been playing a lot with the dimension $27$, let us recall the one universal Koide phase, in the form $\phi = 1/9 \pi$. This is the usual $2/9$ phase divided by $2 \pi$. As it happens, the fraction of baryonic matter in our universe is exactly
$\Omega_b = 1 - 27 \phi = 1 - 3/ \pi$
as predicted by Louise Riofrio many years ago, and recently confirmed by WMAP. The $3/ \pi$ is a dark matter fraction. It may be thought of as an inverse sixth root of unity, where $6$ labels the dimension of the (dual) tetractys neutrino path space.
6 years ago