hylarchic, I believe, refers to "having a wooden head"

Not true, it's solid granite, with a little tunnel drilled through so you can see light if you look in my ears.

As to the true sense of the word, ignore tsuwm and his reference-dependent comrades-in-words: a hylarchic system is one in which things are organized just the way I like 'em. Sadly, it is purely theoretical.