. Except with a qualification on this statement: "The appetitive and the spirited parts, like the workers and the guardians in the Kallipolis, are under the rule of reason (the philosopher-kings). The just individual will be so because reason rules and appetites are kept in check."
I would substitute guardians for auxilaries, as Plato's definition of the guardians changes in the book. The guardians are the group that produces the philosopher kings at the end stage.
So, Producers = Appetitive
Auxilaries = Spirited
Guardians = Reason (with the philosopher kings being produced out of this group)
As well, Spirit aids Reason thus keeping the Appetite in check. Just some minor details.
The whole problem with this is that it isn't a definition of Justice. Plato (or Platocrates :P) is just describing a just city and (by analogy) a just person. But we are still lacking a definition.
At the moment I am interested in definitions. Can a definition ultimately be an example at the most basic level? Would we say this is the case with respect to God and morality?