Redemption Capacity Function

Definitions

Variable	Definition
$\LARGE\Xi$	ETH
$\Large\xi$	ETHtx, native weiWard token
$\Large P$	Price of ETH gas ; $\LARGE \frac{\Xi}{\text{gas}}$
$\Large C$	Collateral Ratio ; $\LARGE\frac{\Xi_{\text{ on AMM}}}{\xi_{\text{ off AMM}}}$
$\Large \gamma$	ETHtx Scalar Quantity ; 21,000 $\LARGE\frac{\text{gas}}{\xi}$
$\LARGE\psi$	DEX Shield ; 0.925 ; 7.5% redemption fee, consistent with transaction fees

Relations

One ETHtx (ξ) represents 21k gas (γ). ETHtx may be converted into ETH (Ξ) using the gas price (P):

$$\LARGE{\Xi = \gamma \xi P}$$

When redeeming ETHtx, a realized gas price can be calculated from the amount of ETH received (Ξout) after redeeming an amount of ETHtx (ξin):

$$\LARGE\frac{\Xi_{\text{ in}}}{\xi_{\text{ out}}} = \gamma P$$

The collateral ratio (C) may be calculated by comparing the contract’s ETH supply (Ξ on AMM) to the contract’s ETHtx supply (ξ outstanding):

$$\LARGE C = \frac{\Xi_{\text{ on AMM}}}{\gamma \xi_{\text{ oustanding}}P_{\text{current}}}$$

Redemption Capacity Function

$$\LARGE \frac{\Xi_{\text{ out}}}{\xi_{\text{ in}}} = \begin{cases} \psi\gamma P_{\text{current}} & C > 1 \\ \psi\gamma P_{C} & C = 1 \end{cases}$$

Graphical Representation