ETHmx and ETHtx Minting Functions

Collateral-based Liabilities Expansion

$$\Large \zeta = \frac{\zeta_{\text{floor}}}{\zeta_{\text{ceiling}}}\left(\frac{C_{\text{cap}}-C}{C_T}\right) + \zeta_{\text{floor}}$$

$$\text{ Where, } \\ \text{}\\ \zeta \text{ is the ratio of ETHmx minted per ETH contributed, } \\ \zeta_{\text{floor}} \text{ is the minimum ratio of ETHtx minted per ETH}, \\ \zeta_{\text{ceiling}} \text{ is the maximum ratio of ETHtx minted per ETH}, \\ C_{\text{cap}} \text{ is the end-of-range collateral ratio} , \\ C \text{ is the real-time collateral ratio on the weiWard AMM, and} \\ C_T \text{it the target collateral ratio; 2}$$

$$\Large P_{\text{mint}_{\text{ETHtx}}} = \left( \left(\sqrt{\frac{C}{C_T}}-1\right)^{-1}+\mu\right)P+P_{\text{min}}$$

$$\text{ Where, } \\ \text{}\\ P_{\text{mint}_{\text{ETHtx}}} \text{ is the minting price of ETHtx in Gwei, } \\ C \text{ is the real-time collateral ratio on the weiWard AMM,} \\ C_T \text{ is the target collateral ratio; 2,}\\ \mu \text{ is the collateralization scalar; 5,}\\ P \text{ is the current ETH gas price on the AMM, and}\\ P_{\text{min}} \text{is the minimum possible minting price of ETHtx in Gwei}$$