[cruegge]

> Yes, I thought this was clear from my statement.

Yeah, sorry, wasn't really necessary to repeat that point. I was too focused on the "limiting the height of the tree to 32" formulation.

I have to admit that I don't quite understand what invariants along the lookup you mean. All lookups that reach a particular node on level 32 have the same hash, so regardless of how you compute the branch from the hash below level 32, they will always follow the same path starting from there (except for terminating at different levels, obviously). So nodes only ever have one child at most, and there's no loss in simply picking child 0 in all cases.

Sorry if what I'm describing is again obvious, maybe I just don't understand your point correctly.