AuT-pp 17 converging and diverging infinite series without convergence

Space has built in convergence (0,1,1,0,1,1,0)  Whether you have a single space solution in the algorithm or thousands, they all converge on zero. Divergence is having two going to positive results while only one goes negative at any one time overall, but they still converge towards zero.
This algorithmic effect of the F-series is carried over in the infinite converging series that makes up dimensional space, but it is fundamentally different as well as being a precursor.
The "geo" function which involves the evolving solution of pi suggests the following:
Pi is F(n)!; that is it is the sum of a function of n over all the individual values of n in the universe for different informational (ct) states.
This may be seen as follows (except that space doesn't have dimension and hence the function is found a a precursor to the other functions):
n/n^0+/-2! or
1/(1)+1/3-1/5...  If you look at this in terms of space it makes sense using the f-series 0,1,1....(2,3,5,8).  The reason is that you have zero (irrelevant in our math, but critical for purposes of the built in convergence) then you have 1 (1/n^0+1) and then you have 1 again (1/[n^0+(1+1)]) then you have convergence which results in the negative as the two 1(s) go to zero).  This hold true in subsequent geometric functions:
2+2/3-2/5...
3+3/3-3/5
4+4/3-4/5 (our version of pi)
5+5/3-5/5...(ct5 or black hole pi)
In each case these go out based on the proximity (in order not distance) of the solutions of the various informational states making up pi.
This solution carries over as convergenece for higher states as the amount of information increases which we refer to as converging and diverging infinite series leading to a universe with compresssion plus divergent (decompression) states.