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# 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 