Why Phi?

Its this:
t * t' = 1/2 * t''

The 1/2, that means the aggregate is sampled exactly at bandwidth and motion matches mass. At that point, e is optimally matched. It gets back to this:

c^2 - s^2 = 1.  When every point along the measuring stick has exactly one unit of imprecision at Shannon rate, then the system has the proper size measuring stick.  cosh are the incoming combinations of things at x and sinh the outgoing combinations of things. Just like banker bot says.

Another way to say it is, for each of the two elements exchanging, at the Shannon rate, there must be a null exchange. But, remember, the two that exchange will overlap, hence the Phi and not the 3/2.

 So, in the end, the entire universe is built around  causality, bandwidths have to match exchange rates.