As I didn't run simulations, I was worried about how would the width vary for different loads on the network. I want users to be able to reference many parent transactions if the braid is getting "thick", and reference only one if the braid is a chain. What would be the rule for the client wallet to decide ? As processing a transaction having many parents has a cost to the network, then this amount must be linked with the transaction PoW somehow.

I read your post and some other posts about this same matter the last months, so I decided to publish my old draft paper, so that others can use those ideas. But I'm not actively working on it.