Any of you big brains know if there is a short formula expressing a cyclic-universe, or just a cyclical system in general that I can plug stuff into?

Doesn't haven't to be proven.
Even if it's only theoretically/mathematically expressed like White-Holes or something, and is probably fiction.

Something to express all the energy in an enclosed system being compressed to a single infinite point.
(I know our current understanding of entropy suggests that it's unlikely and that no more work can be done at some-point, but this is assuming there were some extenuating force - a quantum/thermal fluctuation, gravity acting odd, etc.)