[Bill S (OP)]

This alone could suggest one of two things, namely that the “arrow of time” surely has more granularity to it, granularity that features a “golden-ratio” algorithm.....

Would I be right in thinking that you are using granularity in the 2nd sense, below?

granularity
1.   the quality or condition of being granular.
2.   (Technical)  the scale or level of detail in a set of data.

[phyti]

faster than light.jpg (52.7 kB . 925x588 - viewed 866 times)
I have a reference about tachyons, and the strange perceptions resulting when considering the axis of simultaneity.
In fig.1, the tachyon (red) is moving at 2c, which happens to be the Ax axis (established using the SR clock synch method). The tachyon has moved from the origin to the end of a stick 3 units long, triggering a photon emission (blue). A concludes the tachyon detection at the origin and the photon emission were simultaneous.
In fig.2, a rumor (red) moves instantaneously along the stick, triggering a photon emission at the far end. A concludes the photon was emitted at -2(.866)=-1.73, before the rumor left the origin!