Picoseconds II

For any power law mass triple $(n^2,n,1)$, such as $(4,2,1)$, the Fourier 2-cycle $F^2=\left(31\right)$ acts as a T duality operation, inverting scales. That is,

$F^2:(4,2,1)\mapsto (1,2,4)=(\frac{1}{4},\frac{1}{2},1)$

where one can keep the total mass scale the same through a T duality coupling of $n^2=4$. Recall also (from mid July, Tommaso) that the vector $(1,4,2)$ appeared in the eigenvalue equation for a full six dimensional standard model operator, with the eigenvalue an elementary 3-cycle, using mod 7 arithmetic.