Negative. Cashu does not sit on top of lightning. It's protocol is agnostic to Lightning and Bitcoin. Reference implementations of Cashu however do put a dependency on lightning for interoperability and integration to make lightning payments. But this is not a core principle of Cashu itself. Users need to be aware that when they accept a cashu payment, they are NOT holding Bitcoin but rather IOUs. If the mint is honest, it will allow exchanging those IOUs to pay lightning invoices presented.

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FWIW, Lightning doesn’t sit on Bitcoin either. You can put it atop any chain. I get your point, but the value for Cashu (the current implementations) is due to the network effect of Lightning. And yes, like cash, they are transferable IOUs. AFAICT, I am not aware of any non-Lightning implementations of Cashu - I would call these more generically Chaumian mint implementations

NUT-04 (mandatory) has a reference to Lightning. So maybe we should be discussing #CashuBTC versus a more generic #cashu that you are referencing.

Then the mint is my custodial. Thanks, I'll check that. Curious how to set up a mint - close to my lnd and bitcoin-core.