We have proved that gravity is not constant

I think our connection between combinatorics and calculus leave us with some facts. In a spherical world, equations greater than the third differential will not work with a universal constant.  The combinatorics limit Stokes theorem; hyperbolic functions of greater than third order will not have the combinations to meet Stokes.

So, the N-Body orbits, with a constant gravity, have no solution when N is greater than four because gravity cannot be confined to a value less than some rational bound.  Hence, we have to use local wave methods, and these methods maintain a local gravity with finite travel time. This is all related to the limits of sphere packing.

This value: 5*(1−tanh(n)^2) *tanh(n)^4 gives us the coefficient on the fourth differential in combinatorics. When we subdivide n into a more divisible 'ruler', we reach the point where tanh(n)^2 does not change more than n. So the difference in the order differentials is not noticeable.  So it is fundamental, to counting which is simply a method of integer indexing values. At some point the values change faster slower than the integers are subdivided. Differentials are integer indexed. Minimal redundancy tells us that at some point delta log(n)/n is less than 1/n. Another way of stating the problem is that the natural log does not gain accuracy with n as fast as other variables. So adding another quant level makes the value of some differential the same with an increase in quant. That ends up being a divide by zero somewhere in calculus. Let's reformulate the natural process. The fundamental goal of nature, anywhere, is to estimate the value e, or log, such that the system is stable. But that estimation is limited by the differential order of the system. An N-body system where N > system order, cannot find a global estimate of e more accurate than the local estimate.

There are whole classes of problems that we can determine solvability if we can bound the combinatorics via some quantization method. Tanh is a very powerful indicator of measurement bounds. It is fundamental to counting.