The place for leftist memes

Capitalism is an emergent property of human behavior

This sounds deep at first, but upon thinking for a second is a truism on the lines of "that's just the way the world works". Everything humans have done as a society is an emergent property of human behaviour. Capitalism, mercantilism, fascism, communism, anarchism, feudalism, slave society, empire... and so on. These are all also emergent properties of human behaviour.

It didn’t fall out of the sky, we invented, of our own will, and to the peril of many.

This also is just a truism. Yes, of course it was invented. It's a social system. These aren't inherent. I didn't claim otherwise.

How can any collection of humans, however organized they may be, prevent whatever their ideal state of anarchy is from changing into capitalism over time?

...By being organised and connected and educated. A society that has managed to erode the state and revolutionise society to live without hierarchy would be fundamentally different to the one now. To extrapolate behaviour in that society based on any behaviour you see in this one is fraught and must undergo further analysis based on the material conditions. But, based on anarchist, communist etc theory I've been exposed to thus far, such a society would not even by tempted by capitalism because - what is the point? We've moved past that. It's in our history books and we look at it the same way that today we see feudalism.

I feel that it’s a very important question for anarchy because if any society wishes to have its members enjoy max freedom, the very first question that should be asked is “are we defining a cap on freedoms, or are we not? If we do, should we enforce it, and if so, how?”

This seems rather loaded. What do you mean by a "cap on freedoms"? Right after mentioning capitalism, it seems you're equating capitalism, or maybe the concept of private property, with freedom.

the subtext being how to execute the answers without immediately establishing a state. (This you stated, essentially, and we agree)

There is no need for a state. People can organise together and make decisions together, then disperse to execute those decisions.

And keep in mind that what I may or may not know doesn’t impact the question at all.

Not sure what this means or how to address it.

How does anarchy survive the human condition, and humanity’s predispositions?

Define for me the human condition, and what you mean by humanity's "predispositions". These are not solid concepts.