But who decides the morality in a anarchist culture? You have laid out some some values by which you say an anarchist lives by, and which a statist lives by, but how it this morality decided? Further how does that culture grow without authority?

I guess my question is what are the guiding forces of anarchy that separate it from chaos?

As for burden of proof, this is the ultimate question of the clashing of any two or more cultures. You are describing an area where anarchy and statism are incompatible. Statism draw some lines to create rules in order to work as a system and anarchy as you describe it has much more personal barriers. At this place where the compatibility crumbles the burden of proof defaults to something more primal, and this is the violence that you speak of, who has the power to enforce their own truth?

It's clear that you don't like this position, it seems unfair and immoral. What is the solution?