Before revision:  We also prove that Martingale Fishmonger has   an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.
After revision:  We also prove that Martingale Fishmonger has transform is optimal in the non-mergeable world, and that an MVP of around 1.63 , and conjecture this to be an information-theoretic lower bound on the problem, independent of update time.