### Picoseconds II

For any power law mass triple $(n^{2},n,1)$, such as $(4,2,1)$, the Fourier 2-cycle $F^{2} = (31)$ 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.

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

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.

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