FXS1559

FXS1559 calculates all excess value in the system above the collateral ratio and uses this value to buy FXS for burning. Every AMO proposal must include an FXS1559 function which calculates how much value over the collateral ratio (CR) there is accumulated. This value goes to burning FXS. 
FXS1559 is named in homage to EIP1559, the Ethereum improvement proposal which burns ETH during block production given certain gas prices/usage metrics. EIP1559 has completely changed the ETH native asset's value proposition and formalizes value capture on the protocol level. EIP1559 tightly binds ETH's economic value on the protocol level. Similarly, FXS1559 binds FXS value capture on the AMO level. Because AMOs have an infinite, Turing-complete design space for conducting any market operation strategy, it's important to formalize how FXS captures value across every possible AMO design. 

Specifically, every time interval t, FXS1559 calculates the excess value above the CR and mints FRAX in proportion to the collateral ratio against the value. It then uses the newly minted currency to purchase FXS on FRAX-FXS AMM pairs and burn it. 
Example: 
There is 100m FRAX in circulation with $86m of collateral value across the protocol at an 86% CR. The system is in equilibrium with FRAX trading at $1.00. Collateral is deployed through multiple AMOs, such as the Collateral Investor AMO and Curve AMO. The various market operations of the protocol earn yield, transaction fees, and interest. Each day there is $20,000 worth of revenue earned from various AMOs. This would increase the CR by .023% each day since it is a surplus of $20,000 of collateral value. After t = 24 hours, the CR is now 86.023% which is higher than the 86% target. Given that the CR is 86%, the protocol can rebalance to the CR in two ways. It can use the $20,000 worth of collateral profit to purchase FXS from AMMs. However, a more efficient and advantageous method is to mint 20,000/(.86) = 23,255.814 FRAX

It then takes the newly minted 23,255.814 FRAX and purchases FXS from the most liquid onchain market(s) (currently the FRAX-FXS Uniswap pair). The FXS is then immediately burned. This second method has the distinct advantage of expanding the FRAX supply, accruing value to the FXS token holders, as well as rebalancing the protocol to the CR.  

Essentially, FXS1559 is an in-protocol rule for every AMO to formally channel excess value above the current target collateral ratio to FXS holders. 

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