Consider embedding the topHat id into the id of its child hats
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spengrah commented
The current pure integer approach to hat ids is dead simple, but the result is that identifying which topHat a given Hat is associated with requires traversing the full hat tree back to its root (the topHat).
An id scheme that combined the topHat id with the hat's id would enable much easier and more flexible identification of a hat's domain (ie topHat).
Even further, perhaps a Hat id could include information about the entirety of its own branch of its hat tree??