I feel like we should be doing something with accumulators in Cashu. Accumulators are just so darn efficient. 

Say the mint would offer an accumulator of all spent ecash tokens (a bloom filter for example). The wallet could download that few-hundred-byte accumulator and immediately check all ecash for its spent state. If the accumulator check says "not spent" – we're good. If the accumulator says "spent", the wallet can't be certain that it's not a false positive and would do the usual check with /checkstate.

This isn't the best thing you can do with accumulators. There might also be an avenue for checking the spent state of ecash when you receive it while being offline. Suppose a user has a relatively up-to-date accumular downlaodded from the mint. This accumulator can be used to check all ecash produced before the accumulator for its spent state. Would be super useful for offline transactions. Downside: it can't cover ecash minted after the accumulator update. It might need some additional fancy crypto to prove that the user is receiving ecash that was minted before a certain date, so the receiving user can be sure that it would be covered by the accumulator. 

(Edit: I think you could also prove the creation date of a token without too much crypto magic. if the mint would give the user a signature on the message "I signed the blinded message Y on date `date`" this signature could be transferred from user to user as a proof of mint-date)

#justAccumulatorThings