It is impossible to prove a "For all" through simulations.

Agreed; my hypothesis under test concerning the historical attempts at self-rule governance is axiomatic. The part that I can measure is whether or not fractally's design prevents collusion.

Also, the so called equations of motion will need to incorporate some probabilistic variables

Agreed, and a good point. The approach I took in the simulator's design is mostly based on those elements of evolutionary game theory that also describes the equations of motion in some well known phenomena in condensed matter physics (i.e. statistical mechanics). I have an article in progress that demonstrates these concepts that I will publish soon.