Saturday, December 10, 2011

Back to Koide V

A brief note for those who are following proceedings. In allowing paths through all eight quadrants in three dimensional $XYZ$ space, we can see the geometry of $(b,c,s)$ type quark triplets (with the correct Koide eigenvalue signs). We can also split the central (six path) vertex on a tetractys into convenient subsets. For instance, take three separated $1$-circulant paths ($XYZ$, $YZX$ and $ZXY$) in the quadrant $+++$, and the three separated $2$-circulants in another quadrant. Recall that although we start with diagonal ($\sqrt{m}$) space, the Fourier transform will take us to the circulant space and back again.

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