> Surely a proof that you can withdraw a certain amount of bitcoins is more-or-less equivalent to that many bitcoins, and therefore any rational actor - includi

> Surely a proof that you can withdraw a certain amount of bitcoins is more-or-less equivalent to that many bitcoins, and therefore any rational actor - including your suppliers - should accept it as such? The problem is fees. If this rational actor has 10,000 proofs of payment from as many different people, then the settlement transaction might require the redemption of up to 10,000 inputs, which would make payments prohibitively expensive. It may even be impossible to settle in a single block, since the transaction (including dependencies) might exceed the maximum block size. A proof that 0.001 BTC can be withdrawn at any time isn’t very useful if the cost of withdrawal is 0.001 BTC. In other words, LN surely has the value transfer part solved. But I don’t see how it solves the clearing part, that is: grouping multiple payments from different clients into a single, low-fee Bitcoin transaction. I understand how fees are saved on multiple payments from the same client (that’s what a payment channel does), but not how it would work with payments from many different clients (which is what merchants need to handle).