About the N-body?

We have a general method, I think. Write the finite element digit set, and make a ring. From there we get a bounded short order polynomial.  The standard  n is  the quant angle and appears in the exponent of base b.  Make a reversible transform and you get a standard polynomial, with sufficient roots.

So what is the N body polynomial for a unit world?
In my spread sheet, I have it as each gravity body adds and subtracts a vector of gravity while stepping quants. But the thing is, the distribution of things do. In the tanh world we can do that, count the distribution; and do Newton's calculus.

So, the N-body, you get the standard N-body motion,
P(N) = b^ [3 a * n] + b^[2 a * n] -b^[a * n] +1 = 0, 

in my simple one based world.  We use  roots in N body, but we are allowed to approximate then with rational ratio. So you make a little rational fraction, recursive,  machine, in the base b set of things to do. Write the rational as bounded, but improving.

A simple n = almost pi/2. It counts any rational ratios needed. Powerful tool.

So, we should be able to get a P(t) in some short order polynomial and it counts things we might do, someday, with a quant of n.

But, its a bounded, polynomial solution adaptable to both time and distance.  I have no doubt none of the universe works unless it has soldiers doing the finite stepping everywhere. We have to make the value ln(b), it is always needed. Make it from an optimized polynomial in the quant n. We make a specialized base because we get the algebra without the redundant stepping.

It a run time encoding machine with adjunct spectral polynomials. You get wide latitude when you separate groups with tanh. Two and Three and separate polynomials can be combine with controlled coupling. Bournilli freebie. Easier than the Shannon, and just as effective; and we get recursion, as a bonus and that means a exponent base tuned to the recursions of motion. The proton really does this. We know the quark polynomial  will be like the one above.