Can you explain the offline part without having the possibility to invalidate the token from the mint ?
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sender has cash in their pocket and hands it over to receiver. receiver needs internet to re-issue tokens to prevent double-spending.
alternatively, if only the sender has internet but receiver not, sender can lock the tokens to receiver's pubkey and send over.
one of the both needs internet to fully prevent double spending
Do sender and receiver have to be using the same mint?