The problem is simpler than I thought

We have already orthogonalized the power series for four different unit spheres. That means we have solved the roots, made the map, set the quants, incorporated the noise bounds. And we included the 'do nothing' count to accommodate maximum bandwidth.

For any given quant N, then, all we need to do is find the up/down direction for four different counters to minimize phase at that quant. Sounds much easier, very little hassle except finding all the roots. None of the roots are changing, so we have no partials really to worry about except the partial of one quant to another in a different counter.

The geometry is greatly simplified with a discrete Reimann surface.  The polynomial recursive roots are the eigenvalues of the system. I am pretty good at this!