How is the fair price calculated?

Stablecoins are in and of themselves not stable since they are directly pegged to fiat currencies that do not necessarily retain purchasing power. Another point in question is the 100% or more reserve requirements, which bring about capital allocation inefficiencies and limit the scalability of any of them. We’ve worked around Nash’s idea of “ideal money” in a decentralized network.
1) We posit that for private monies (see the work of Klein in 1974 on this topic), money issuance should be costly to print to incentivize minters to control for inflation – especially when supply is uncapped like in our case.
2) Miners are profit-oriented.
3) The only known reliable data in a PoW system is the difficulty D.
But D is nothing but the energy cost required to print one coin if the block reward is proportional to the computing power allocated to the network. In that way, our chain is measuring the average cost of electricity spent for each coin (this cost can be controlled by a k-constant voted by miners to take into account for the productivity gains in the energy sector).
For simplicity, let’s assume the cost of production of 1 JAX is $0. The opportunity cost o(c) of mining JAX is then determined by o(c)=(〖(P〗_BTC∙6.25))⁄D, where P_BTC is the spot price of BTC at time t. This is the upper bond price of JAX above which it becomes not economical to print this coin. Since the cost of production is non-zero, the price can only fluctuate within this narrow band. Volatility is controlled this way, and as long as the opportunity cost is higher than the dollar, value is retained against fiat.
The following hypothesis needs to be obviously verified, but if realized, volatility is further controlled. Thanks to arbitrage, it becomes more profitable for miners to print JAX rather than Bitcoin when the price of the latter goes down. With merge-mining, they can switch their hashrate towards printing JAX at no cost. Hence, keeping the total hashrate much more stable than it is now, and further reducing the narrow band within which JAX can fluctuate, since D will remain more stable during demand shocks. In a nutshell, printing JAX is then entirely a market-based mechanism and an arbitrage.
Thus, the governor has the duty to set the “fair price” of the pair WJAX/JAXUD. This fair price is calculated as follow:
K= (P_BTC*6.25)/D
With, P_BTC the market price of Bitcoin at time t, 6.25 being the current block reward – excluding the transaction fees, which are anyway distributed whether you print JAX or BTC+JXN – D is Bitcoin network difficulty.
However, in order for the market to find the price equilibrium of WJAX, we allow _deposits and _withdrawals within a range, such as:
K= (P_BTC*6.25)/D ∓ε'
and ε' is a margin term to allow some price fluctuations and more market arbitrage for the WJAX/BUSD price, and where ε^'∈[0,0.1]. In other words, one can deposit BUSD in the contract up to the limit of K+10%, while withdrawals can be proceeded up to K-10%. Because both D and BTC hashrate are fluctuating, and miners’ costs are asymmetric, we allow for some deviation for the fair price to incentivize deposits. Withdrawals can therefore be done at a loss if the deposit price was higher than the withdrawal price, but this is at the entire discretion of the staker. To a certain extent, we also allow withdrawal at a potential loss in case of external shocks.