The differences between the ESD model and AMPL can be summarized in two points: the use of a Time-Weighted Average Price (TWAP) algorithm to make oracle prices less susceptible to manipulation and to more smoothly adjust the market. Additionally, it introduces mechanisms for debt and coupons, making it relatively more complex. The essence is to incentivize users to actively participate in adjustments.

First, unlike AMPL's daily rebase, ESD uses a USDC-ESD liquidity pool on Uniswap (a decentralized exchange) as its price oracle. The supply of ESD can continuously expand to ensure the quantities of ESD and USDC in the liquidity pool remain equal, thereby maintaining the value of 1 ESD at 1 USDC (or 1 USD fiat currency).

ESD operates on an 8-hour cycle, with each 8-hour period called an epoch. At the transition of each epoch, the ESD smart contract checks the price of ESD tokens. ESD employs Uniswap's TWAP algorithm, which calculates the weighted average price over the past 8 hours, making it significantly harder to manipulate the oracle price. The ESD price is also not evaluated at the instantaneous boundary of an epoch to avoid manipulation.

Furthermore, ESD introduces debt and coupon mechanisms instead of directly increasing or decreasing supply. After a rebase, if tokens are to be minted, ESD holders must stake or provide liquidity to receive the newly minted ESD. If deflation is needed, it is not done directly but by attracting more capital through bonds.

For example, when the ESD price is above the peg (1 USDC), users can choose to stake their ESD to earn newly minted ESD rewards, akin to passively earning yields through liquidity mining. This increases the circulating supply of ESD, thereby lowering its price.

When the ESD price falls below the peg (1 USDC), the ESD protocol issues debt, which token holders can purchase. ESD issues coupons, and holders can burn ESD to obtain these coupons. Purchasing coupons comes with a discount, and as debt increases, the discount grows, incentivizing holders to burn more ESD and buy coupons. This reduces the token supply and raises its price. In the future, if the ESD price rises above the target (1 USDC), coupons can be redeemed for more ESD. However, it's important to note that coupons have an expiration period—they expire after 90 epochs (equivalent to 30 days). Failure to redeem them within this period results in a loss.

Clearly, this mechanism incentivizes arbitrageurs. When ESD is above the peg, users can passively earn yields by staking their ESD. When ESD is below the peg, users can buy coupons at a discount for the chance to acquire more ESD in the future. Of course, buying coupons carries significant risks and is not suitable for everyone. Thus, the ESD model is more complex and better suited for professional players engaging in arbitrage.