They are not really connected, you could even have a lightning node with less funds than there is ecash. I believe nostr:npub12rv5lskctqxxs2c8rf2zlzc7xx3qpvzs3w4etgemauy9thegr43sf485vg is working on a proof of reserve mechanism so that users of the mint can verify if a mint is backed.
Discussion
Got it
So the mint can technically mint and burn at will, it’s just that the Cashu implementation does this with LN sends and receives
I’m assuming it’s similar with fedimint but also including on-chain?
So from a very literal standpoint the ecash is an IOU from the mint, and while in practice this redemption is meant to be automatic and programmable, this functionality can be broken (by for example a bad actor or just code bugs, etc)
I say this to distinguish it from LN which has a redeem-ability that generally speaking can’t really be broken (it’s MUCH more trust-minimized)