Sure, sorry to both you and @calle if I was unclear, I obviously do understand that only the receiving party (say, merchant) has to be online/contact the mint. I still think that it is an extremely bad architectural feature that each transaction requires such an online message *to a central party* to be sent. Btw it's important to note that many of the early papers (say 1990 period) on ecash were discussions around achieving offline payment, i.e., avoiding this problem. There was one paper that Chaum co-authored with someone else and there was def one by Brands, probably tons of others. They all focused on an idea of "proved fraud" in case of double spend, thus they used punishment mechanisms. I discussed this quite a lot in the early part of my talk in London, because I thought it was a pretty fascinating issue.