Fine structure as a flat earth error term

Take the triple and compute a fourth color, called temperature.   The hing will count at the Shannon rate and the Lie hyperbolic surfaced flattened to the unit circle. But i should generate photon emission of the proper color complement. The fine structure, the implied error, is treated properly, I think. The 1/137 should have a relation to Avogadro.   But the relativistic effect is increase curvature.  Maybe related to the 4D version of Avogadro.