I probably shouldn't use the word "bond" to describe the big bond, but I am no wordist. I don't know what to call it.
Flying Fox has 2 types of bonds.
The first is an inaccessible safety deposit that the blockchain can take away at any time to punish a mistake. This small bond is a bond. It is used to punish validators who validate on contradictory blocks. This money is not in a channel, it is locked up and inaccessible.
The second bond is used for voting purposes. It is measures a distribution of users who are as similar to the distribution of value holders as possible. This money is accessible. So "bond" probably isn't the best name for it.
Most proof of stake systems today use the same distribution of coins to act both as the small bond, and the big one. I show in this paper, that using the same distribution of coins for both of these goals is inefficient. The portion of value being bonded is either too big for the first goal, or it is too small for the second goal.
I don't understand the dual use of the money. If my money is in a channel, I can send it away to Person B, at any time, off chain. However, if my money is securing the blockchain, then these funds are "staked", so that the blockchain can send it away from me (to Person C) if I make a mistake.
Yet, the same 1$ can't go to both B and C. This seems to be a contradiction.