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A triangle ABC of lightning nodes opens a channel with 1 bitcoin between nodes. 3 bitcoins total.

Each node can have a state with a total of 2 bitcoins. That's 6 bitcoins.

It'd be a race to close channels, and only if the channel value is above the fee-floor, else the settled value is $0.

> A triangle ABC of lightning nodes opens a channel with 1 bitcoin between nodes. 3 bitcoins total.

>Each node can have a state with a total of 2 bitcoins. That's 6 bitcoins.

Well, no. If you want a channel between A and B with 1 BTC capacity in either direction, you'll need to deposit 2 BTC to fund the channel. Therefore there's 6 BTC total that's locked up. As for the rest of your comment, it's not really clear how it's "separated" from the on-chain value.

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