I glanced over the paper and have a couple of perhaps naive questions:
1. As bitcoin has economic value, I don't quite understand how this would work with sidechains. Suppose I transfer 1000BTC to a sidechain, but whatever changes i make will result in a loss of purchasing power of the "new bitcoin" in my sidechain. However, since I have a two way peg, i would be able to transfer my "new bitcoin" back to parental bitcoin chain at the 1:1 ratio?
2. Alternatively, if my "new bitcoin" chain will be successful, then bitcoins will 'evaporate' from the parental chain toward my chain, but it is intuitively unfair that initial coins in the "new bitcoin" will have the same value as latecomers 'new bitcoins' that will 'evaporate' later from the parental bitcoin. If no equal value, then how that difference in value would be determined?
3. Will parental bitcoins acquire more and more value as sidechains accumulate or will they lose value toward zero as value is transferred to sidechains?
4. I think that authors might need to introduce some value "entanglement" between 'locked' bitcoins (that moved to sidechains) and the rest of bitcoins in the parental chain. This way, if sidechains acquire additional value this value will be reflected in "non-locked" parental bitcoins, otherwise parental bitcoins will be unaffected by sidechains growth and will eventually lose value.
1. Not sure why you think bitcoins will lose purchasing power on your sidechain. Because coins can always be transferred between chains, the value will be roughly equal. Any difference in value will be small and will just compensate for the delay in moving them.
2. Not sure why you think coins on both chains having the same value is "unfair." But again, the values will be roughly equal, because if they weren't there would be a profit opportunity in buying coins on the lower value chain, transferring them to the higher value chain, and selling them. Similar to why bitcoins on (functioning) exchanges tend to be about the same price.
3. As described above, the value of coins will be roughly equal between chains.
4. This is unnecessary. Market forces will make the values approximately equal without needing any help.
Purely economic discussion about sidechains should probably be on the 'Economics' subforum.