We have to do Maxwell in finite polynomials

c becomes the Higgs sample rate relative to the vacuum, which is also a polynomial, of order 1 or 2.  E and B come from the atom, they already are bandlimited to the fundamental sample rate of the orbitals

The Laplace operator need only have an axis along the line of travel and one radial axis. But the polynomials B and E have to carry the vectors induced by kinetic motion. The vectors are identified as [pi/3 or pi/6] and so on, is my guess.

If r is the most irrational number and b=1/r the fractional count, then the vacuum, against which you differentiate, is of order b^2, if you want to try curved vacuum, or b otherwise.  Higgs is b^107, by my calculations.  There is that one self symmetric Boson that makes gamma around b^99 or b^104.  The visible light is all b^15 to b^17, with exponents to three or six; depending on the game you play with the quarks. I think all the differential come out as division, actually, and everything should divide OK, I would think. We end up with a digit sequence that coutns out fractional units of 1/Higgs.

The only thing different from the analog version is that we never entered the world where irrational numbers prevail, except for b.