The theory can handle multi-path payments, but not the kind of multi-step thing you propose.

(It should be noted that your proposed method for getting 2 btc from A to D requires a change in the wealth states of other nodes.  Still no direct payment of 2 btc from A to D that leaves the wealth of other nodes unchanged is possible)

SimpleStacker

Very good review! I was going to read the paper, but I kept waiting because I was hoping you'd do a write up and make my reading much less painful...and you delivered!

I wonder how he handled the case of multipath payments. For instance, in the case of the two "rings" of nodes connected by a single 1btc channel, as long as the total capacity for each ring never gets more than 1btc different from the other ring, wouldn't it still be possible for A to send D 2btc? They just need to split the payment in half and wait for some other payment to rebalance the "bridge" channel.

bitcoin

lightning

econ

[Article Review] A Mathematical Theory of Payment Channel Networks

Very good review! I was going to read the paper, but I kept waiting because I was hoping you'd do a write up and make my reading much less painful...and you delivered!

I wonder how he handled the case of multipath payments. For instance, in the case of the two "rings" of nodes connected by a single 1btc channel, as long as the total capacity for each ring never gets more than 1btc different from the other ring, wouldn't it still be possible for A to send D 2btc? They just need to split the payment in half and wait for some other payment to rebalance the "bridge" channel.