What I did with the complex plane

I say I can translate it, rotate it , and magnify it.

So If the unitaries form a basis for the polynomials, I can create the resolution map for the unit circle to some finite size, but choosable. Than I can move  transform that unit circle to match the resolution map of any other polynomial, and from that point is will have the same geometry. The Markov system can be set to resolve all roots with the same precision as the unitary sequence.

A simple idea. Pick any set of s,t p[airs you want. Pick a spot on the 1,x,y Markov that gives you resolution. Then we can close a surface to some resolution over which you functions have bounded error.  AN orthogonal basis set looks relatively prime, Markov will give better resolution.  Your inversion is to match resolution pattern, then transform your basis to that point. A neat idea, I really did not think of it.

If you are not relatively prime on your basis sequence, then just make sure you have a good vertical in your model world and their will be a transform. You can then get your 2D surface with an induced vertical makes a closed shape in 3D.