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1) What is PAX?
PAX is BitcoinDark's Pegged Asset Exchange. It will allow users to lock funds to the value of real-world securities - assets, currencies, commodities and so on. What that means is that anyone will be able to use PAX to invest in stocks or precious metals, lock funds to USD or CNY, and so on, without jumping through the bureaucratic and KYC hoops (and paying the high fees) that are involved when going through traditional exchanges and brokers.
2) How does it work?
The simple version is that BTCD are burned (effectively destroyed) and then redeemed (recreated) in the amounts required. So let's say you want to lock funds to the value of $10 USD, and BTCD is $1. The exchange rate is provided in each staked block by a decentralised price feed. You send 10 BTCD to the designated burn address, specifying when you want to redeem them, and receive a string of 'bearer bits' in return. At the end of the given period of time, you receive BTCD to the value of $10, at the new exchange rate. It could be a year later and BTCD is now at $2, so you'd receive 5 BTCD. Of course, this raises various problems. You don't want to be creating lots of new coins if the value of BTCD drops and you need more of them to pay for the locked funds on redemption. Fixed supply is a big deal in crypto. So, there are various mechanisms to avoid that issue.
3) How is the price maintained?
This is where it gets more complicated. You want to ensure that users receive the funds they have locked, without messing with supply. There are a few ways this happens. Firstly, you can lock funds long or short. So if you think BTCD is going to go down in value relative to the dollar, itmakes sense to lock funds as USD. But equally, you could lock funds as -USD (you think BTCD will rise against the dollar). Leverage is available. The trick, of course, is to make sure +USD and -USD are roughly in balance. That way, coin supply isn't compromised. This is achieved using an incentive system to encourage users to lock funds in a way that keeps the system in balance.
'PAX' Pegged Asset Exchange Project from SuperNET
Interview with Cassius