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

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So if one has internet they will likely both have it.

If there is no cell service or internet this will not work at all?

Imo merchants will most likely always have internet, even in remote locations like a beach or a music festival. As a client, you could simply carry a card, ring, or even an NFC wristband and tap to pay then. Or using a phone and mobile device with Bluetooth, as in this case, might be interesting if you're abroad and don't have roaming. Additionally, it could potentially be even better for privacy in general, since no internet is involved at all in the transmission.

exactly 🤙

Do sender and receiver have to be using the same mint?