What if the exchange function specified that after time/block N, the exchange rate is 1 BTC = 0 Micros ? No more arb.
Not to be pedantic, but the point is that the exchange rate can be defined by "any deterministic function". Seems to me that there are probably many classes of deterministic functions which could prevent value from moving back to bitcoin.
Then I suppose bitcoin would be lost, only affecting users of the side chain. Arb could still be done with micros that hadn't matured. As long as the exchange rate is deterministic and not stochastic.
Not sure I follow. If there's no way to move bitcoin to the sidechain, the arb channel is closed, and bitcoin cannot benefit from increased purchasing power of the sidecoin. This is only relevant after all the sidecoins have been created/unlocked/whatever. Is that what you mean by "matured"?
Maybe I should have said expire. So you are saying the exchange rate can cease to exist after a certain time/block N for the entire side chain? Or, once you convert a coin, that coin cannot be exchanged back after a certain time/block N?