The starting point is the "non-well founded" set.
https://plato.stanford.edu/entries/nonwellfounded-set-theory/
Jon Barwise and Lawrence Moss have written a book, "Vicious Circles,"
https://web.stanford.edu/group/cslipublications/cslipublications/site/1575860082.shtml
from which I got this idea of time:
properTime = (clockTime, properTime)
Next I modeled clockTime using nonstandard analysis:
clockTime = (nonstandardFuture, standardPresent, nonstandardPast)
Here clockTime is a "monad" as that term is used in nonstandard analysis. Around the standard part of the monad, a real number, there are nonstandard real numbers infinitely close.
H. Jerome Keisler has written a book on nonstandard analysis which you can download for free.
https://www.math.wisc.edu/~keisler/
Now I must confess that I don't yet have a license to Mathematica. So I'm probably putting the cart before the horse to bother you like this. I apologize.
LB