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 