Excellent summary @PatrickZuest!
Great to see so many excellent questions popping up.
My question relates to the mechanism you devised to mitigate sandwich attacks, whereby a swap is split into many orders. In the case of sandwich attacks, you were able to show how an optimal order split drastically decreases the profitability of an attack.
What is interesting to me is that there appear to be additional benefits in splitting CFMM orders beyond sandwich attack mitigation. A couple of months ago, we had a great discussion with @tarun on the privacy properties of popular CFMMs, such as Uniswap.
His publication introduced the idea of using order splits to improve the privacy of CFMM users. They propose a model which samples order splits for every swap using a Dirichlet distribution. This makes it incredibly difficult to associate a set of swaps to a single blockchain pseudonym, thereby increasing privacy.
Although this is a very different model than what you have devised, I wonder if there is a way to potentially combine the two and build a quasi Order Management System for CFMMs that can offer both privacy and sandwich attack mitigation.
Is this something you have considered before?