The HT thread has closed, so I expect that this is about to also. So some closing remarks.

Tifft and a number of others found 72 km/s and multiples of this differences in the redshifts of galaxies in pairs, small groups and various configurations. Subsequently Tifft found a that in both the milky way centre frame and the CMBR frame (or very close to each) the entire sky showed a common redshift periodicity. In different samples including different types of galaxies he found various related periodicities of 144, 72, 36, 24, 18, 12 km/s periodicities. Although it was seen as impossible to understand as being true, these results have persisted in all tests that I know of. A number of different researchers who realized the importance of the results if true repeated the analysis with different samples and thoroughly investigated the statistics. To the best of my knowledge there is not a single test of redshifts in a single line of sight that did not show at least one of the mentioned redshift periodicities.

At the larger scale, a number of tests reported z=.043 periodicity (12,800 km/s or 128/h Mpc). This seems to be widely accepted as existing now. Several other surveys reported related values to this such as close to 1/2 and 1/3 that period. Whereas the smaller scale periodicities are wiped out by the common two point correlation function, these longer periods are not. From that, and the fact that we see these periods in the the other two dimensions as a type of lattice, we can safely say that they are real distance periodicities.

However the shorter range periods are different. They are not seen in 3D. This argues very strongly for the Narlikar-Arp hypothesis of atomic frequencies changing in steps due to particle mass changes in time. This produces the observed whole sky pattern in the right frame without any observed distance periodicity in the other two dimensions. It also follows that galaxies are not moving*. Any real motion of galaxies by even 20 km/s would destroy the observed patterns.

It follows from this that all the cosmology based on virial theorum and estimation of mass and behaviour of gravity at the largest scales is not understood.

* Actually the galaxies could be moving, but the restrictions on their movement would be very severe and not at all in accord with any prevailing physics or cosmology theories.