Ok this is too philosophical for me today 😅 in my understanding you are melting cashu tokens to Sats and you are minting cashu tokens from sats. So cashu tokens "represent" an amount of sats (minus fees) but they are not transfered via channels but via mints. In Amethyst for example you can directly melt them to your lnaddress.
Discussion
lol me too. I would imagine tokens as a cluster. So, say you are transacting with cashu tokens, does that reflect an increase/decrease in bitcoin for each transaction ? Or only when you buy and sell (mint and melt) cashu tokens from Bitcoin ?