To define Burning Man is akin to defining yourself.
If you can answer the question, 'who am I', then you have found yourself.
Why do you need BM for that?
BM has no core values.
Values are defined by the very nature of your words instilled upon a belief structure of bias and relief from societal infomercials.
If you learn to value yourself on the playa, then you have found the core values you seek.
They are YOUR values, not anyone else's.
Therefore, BM has no core value system.