The cosmology of Pythagoras appears to have been influences by the Zoroastrian idea of archetypes (Fravashi) or ideal forms of things preexisting the physical creation and serving as a model for it. His notion of the dynamic tension between a principle of order and limit on the one hand (and) a negatively unlimited chaos on the other also echoes the kind of Zoroastrian cosmology that leaves room for Ahriman's deranging influence....Plato claims that archetypes are the absolute standard of the reality of anything else, and he was introduced to this idea through the Pythagorean Order. Plato's argument, in "Republic," that a just society is one that is ruled by philosophers, was also an idea he absorbed as a Pythagorean initiate. The political philosophy that the Pythagorean Order tried to implement in Greek colonies in southern Italy revolves around the concept of Khashatra Vairya (Shahrivar), which harks back to the utopian political doctrine of Zoroastrianism and the relationship between Zarathustra and Kavi Vishtaspa.
Jason Reza Jorjani, “Iranian Leviathan” (2019).