Finite Log(x) should indicate maximum mltiply error

 Our natural finite base must be the finite sum 1/(n!) n from 1 to Maxbaud. Then it conforms to the natural log of the infinite number line. The limit of (1+1/n)^n as n goes to infinity, is e^1. For finite systems, some (1+1/n)^n is the maximum fraction in multiply for Maxbaud n, so this should all work, somehow. The natural base for finite maxbaud is maxbaud+1 taken to the maxbaud power. The error we tolerate in finite systems is the natural e^(1) for n at infinity - the finite x^(1).

In other words, Maxbaud has to be large enough to take the multiply error through one cycle without overflow. This allows for the zero function. In my system, the set of whole parts must be prime, I think. That means each prime must execute the zero function once per cycle. The zero function is the minimum phase  function, it evenly distributes the accumulated error for all digits with the same prime.