The disagreement here seems to be over what constitutes a "solution" for the N-body Problem.. The original prize announced by King Oscar II of Sweden for the N body problem was for an analytical solution. My understanding is that this means that you have a set of equations where you put in the initial values for various parameters (mass, velocity, etc) at t0 and then you can then calculate the positions, velocities, etc at any given value of t, say tn. That is, a single step to calculate the result at tn What you are presenting appears to be a simulation or numerical solution where you put in the initial values at time t and then to get to the value at tn you have to run through a series of steps from t=t0, t1, t2, t3, .... tn.

The original prize announcement by King Oscar II of Sweden:

…. is for a solution of N-body problem with advice given by Gösta Mittag-Leffler in 1887. He announced:

‘Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly.’ See Ref [1]

Here we have taken a ‘a system of arbitrarily many mass points that attract each according to Newton's law’ in Dynamic Universe model. We have not changed the NEWTON’s law anywhere.

And the assumption ‘that no two points ever collide’ is a valid assumption in Dynamic universe model. Due to this model’s fundamental ideology and mathematic formulation the collisions will not happen. But they may happen if uniform density of matter is used. For heterogeneous distributions the point masses will not colloid with each other. They start moving about each other for any formation of point masses as observed physically.

The announcement further says we have to find the ‘coordinates of each point as a series in a variable’, the words ‘analytical solution’ is not mentioned in the announcement. Here in Dynamic universe Model we find the representation of each point exactly from an ‘analytical solution’ derived here in Mathematical Background section (#3) and its Resulting Equation 25 of this monograph. The value of the variables converges uniformly for each point and gives only single value.

 So, the original announcement as stated above says about a series, that should converge uniformly, and it should not give chaotic results. In Dynamic Universe model case, the series converges uniformly, gives a unique value. He did not mention that it should not run through a series of steps from t=t₀, t₁, t₂, t₃, .... t_n. Of course we can calculate the result directly ‘t_n’ with limited accuracy on single time step. In the literature of science, there are many simulation methods for the last 120 years and almost all have changed the Newton’s laws. Some of the recent approaches were using iterative methods with high speed computers. None of them claim that they are singularity free and collision free.

My solution is Equation 25; it is analytical and is derived analytically. Just by saying that Equation 25, is the solution is not sufficient. People may not understand its complexity and depth. To make it understandable, SITA was developed. I want to stress that point again, that SITA is one of the many solutions possible for Equation 25. Many other solutions are possible for this Tensor. Then question comes how to prove and check SITA validity?

The tensor at the equation 25 is subdivided into many equations and calculations are done. Tensor is the basic equation. I am using basic methodology of calculations. It may be called a simulation, but should it be called Calculation? I don’t know. If you don’t want testing of Equation 25, then SITA is not required. I could not find any other method of testing Equation 25.

          This equation 25 can be tested by any person who has pencil and a paper. Depending on the budget available with him, he can use logarithmic tables, Simple calculators, scientific calculators, PC, Laptop, Main Frame computers or Super computers.

          This Dynamic Universe Model (SITA) is NOT a ‘simulation or numerical solution’ when we are calculating the positions / velocities / accelerations of point masses using actual data. It is simply another calculation method. When we use factitious data which is not real or some data used for testing purposes then the results can be called as ‘simulation or numerical solution’.

           It is well known that for N>2 the problem cannot be solved analytically in present day physics. Numerical methods generally mean solving Differential and Integral equations by giving approximation values. Here in Dynamic Universe model there are no Differential and Integral equations. And there are no equations with multiple value results for the same inputs. Because of these two reasons this set is different. This N-body problem thus solved is called Dynamic Universe Model.

            Just giving resulting equations from the tensors will not be sufficient, it will be better to give numerical results also, to see if that matches with reality. SITA is set of 21000 equations, an Excel solution for Dynamic Universe Model for checking these results of Dynamic Universe Model.

            Or else there is no need for a computer. For checking these solutions even a pencil and a paper with a calculator is sufficient.