I am reading paper named "Scalable Funding of Bitcoin Micropayment Channel Networks".
If Alice, Bob, and Charlie created a channel factory, I thought that only these three people can make a payment channel within themselves. However, the paper says "Users will be able to enter the system with one blockchain transaction and then open many channels without further blockchain contact." (page 3).
In the above case (i.e., Alice, Bob and Charlie created a channel factory), Hook transaction becomes 3-of-3 multisig. If Diana wants to join the channel factory, Hook transaction consisted of three peoples already. so I think Diana can’t join in their channel factory.
There is no example in this case in the paper(above picture). Is the way I understand correct ? or not ?
And I wonder how to refund without closing and re-opening ? As you can read in this paper, When a party enters a channel factory, the deposit that the party input is already set at that moment. or.. the meaning of refund in here is moving funds to different channels ?