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 Just so we're on the same page: if both parties are offline the ecash can be double-spent.

CashuMe allows the sender to delete the token upon sending so that the receiver can have more confidence that it won't be double-spent while they're offline.

More: https://gist.github.com/callebtc/67da3f586ef273df80bf679e464bc3f3 
 Fun-fact in double-spending is, that the receivers don't trust the sender 😑  
 Yeah, for those cases one person has to be online (using P2PK for example). 
 ECB promises offline payment without a trace for the digital euro. I am curious how they avoid double spending 😁 
 Black box hw chips. Manufactured at 3nm scale. Nobodys gonna crack that to double spend 100 euros. 
 So merchant and customer, both need ECB hardware? That's a stupid plan. 
 But profitable? 😂 
 Does this only work if you have the right sizes of ecash "bills" (😂) locally? 
 Correct! You could choose to overspend if the amount difference is only small, but essentially that's it. 
 Could it be possible, to use a mint offline? Like people who has ecash already from a mint could communicate with the mint, but noone would have internet?

If I understand correctly, when you use a mint, you anyway trust in it. If you do an offline transaction, you have to trust your peer too. If we can have offline mint usage, I still only have to trust the mint.

What do I miss? 
 You trust the mint but you do not need to trust other users. The receiver of a transaction needs to be online in order to refresh the token they received in order to prevent double spending. If there's no Internet, you need to trust the sender (or all previous senders) and the mint.