Here goes:

A1: Complex numbers exists. Call this C.

A2: x = x

A3: x + y = y + x

A4: A is a subset of B if B contains A and B - A not = the empty set.

Index.....Statement...………………………………………………………………………… ………….. Reason

1...…...….Construct S = C x C................................................. ......................................A1, A2

1.1...…….S is 4 dimensional....................................... .............................................…...1

1.2.........Set the components of S = S_1,2,3,4 in the following order: Re, Im, Re, Im.....1, A2

2......…...S can transform into two Riemann Spheres......................................……... A1, 1

3............Construct two Riemann Spheres in S, call it RS x RS..............................…..A1, 1

4............Isolate the Riemann Circle of S_3, 4 and call it P_T.................................…A1, 3

4.1......…I'm going to use physical terminology below........................................…..De cleration

4.2...…..Construct "physical space" = S_P = CxC/S_4.......................................…...…A1, A2

5......…..Let P_T advance by one (rotate relative to S1,2,3) when encountering a space node and let the rotation be a quantum rotation. Call this "freq" =

T_S......................….............A1, 4, 4.2, A2

7......…..Define "Change in freq" by T_Sf - T_Si…………………………………....5

8...........Let S_1,2 be perpendicular to S_3,4............................................. ....................1

11..........Construct {for all n = 1 to N: n(T_Sf - T_Si)} . Call this "Changes in freqs.".........5,7

12.........Define "basic time interval" = Delta t_B = 1/[(1/N) \sum \limits_{n=1}^N n(T_Sf - T_Si)].................................................. .................................................. .......................1-11, A3, A2

13.......Construct MxT_S, M element of Natural Numbers subset of C..................................5, A4

14.......Define " Basic time" = t_B = {1/[(1/M) (\sum \limits_{n=1}^M n#T_S)]}*Delta t_B.......................12, 5,

A3

15........Couple t_B to every node of S_P and call the result "basic spacetime"= B_ST...........4.2, A2, A2

15.1.....Construct S_i = CxC............................................... .........................................A1

16........Construct RSxRS in S_i, call it Pp................................................ ..................15.1, 2

17........Isolate the Riemann Circle in Pp and call it P_BT.............................................. ......A1, 16

18........Let P_BT advance by one (rotate relative to S_i1,2,3) when encountering A B_ST node and let the rotation be a quantum rotation. Call this "freq2"= T_BST...…………………………………………………………………………………….......... ....................17, A2

19........Construct KxT_BST, K element of Natural Numbers, subset of C..................….......18, A4

20........Define "Tim1" = t_1 = 1/[(1/K)(\sum \limits_{n=1}^K n#T_BST)]..............................A3, A2, 18

21.......Pp is in every particle of the clock............................................. .............................Requirement

22.......Tim1 advances like a clock, it depends on the Pp in the clock and on the route in B_ST.............................................. .................................................. .................................18, 21

23.......Tim1 = Time.............................................. .................................................. ........A3, 22

For the Riemann Circle rotated through any finite amount, infinity is still at the north pole of the corresponding Riemann Sphere.